%------------------------------------------------------------------------------
% File     : Zipperpin---2.1.9999
% Problem  : SEU817^1 : TPTP v8.1.2. Released v3.7.0.
% Transfm  : NO INFORMATION
% Format   : NO INFORMATION
% Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.z8xHOoZiEI true

% Computer : n031.cluster.edu
% Model    : x86_64 x86_64
% CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory   : 8042.1875MB
% OS       : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit  : 300s
% DateTime : Thu Aug 31 19:18:20 EDT 2023

% Result   : Theorem 121.73s 16.25s
% Output   : Refutation 123.15s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SEU817^1 : TPTP v8.1.2. Released v3.7.0.
% 0.00/0.14  % Command  : python3 /export/starexec/sandbox/solver/bin/portfolio.lams.parallel.py %s %d /export/starexec/sandbox/tmp/tmp.z8xHOoZiEI true
% 0.15/0.35  % Computer : n031.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Wed Aug 23 15:42:50 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 0.15/0.36  % Running portfolio for 300 s
% 0.15/0.36  % File         : /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/0.36  % Number of cores: 8
% 0.15/0.36  % Python version: Python 3.6.8
% 0.15/0.36  % Running in HO mode
% 0.22/0.63  % Total configuration time : 828
% 0.22/0.63  % Estimated wc time : 1656
% 0.22/0.63  % Estimated cpu time (8 cpus) : 207.0
% 0.22/0.70  % /export/starexec/sandbox/solver/bin/lams/40_c.s.sh running for 80s
% 0.55/0.76  % /export/starexec/sandbox/solver/bin/lams/35_full_unif4.sh running for 80s
% 0.55/0.76  % /export/starexec/sandbox/solver/bin/lams/15_e_short1.sh running for 30s
% 0.55/0.76  % /export/starexec/sandbox/solver/bin/lams/40_c_ic.sh running for 80s
% 0.55/0.77  % /export/starexec/sandbox/solver/bin/lams/40_b.comb.sh running for 70s
% 0.55/0.77  % /export/starexec/sandbox/solver/bin/lams/40_noforms.sh running for 90s
% 0.55/0.78  % /export/starexec/sandbox/solver/bin/lams/20_acsne_simpl.sh running for 40s
% 0.57/0.85  % /export/starexec/sandbox/solver/bin/lams/30_sp5.sh running for 60s
% 0.57/0.95  % /export/starexec/sandbox/solver/bin/lams/30_b.l.sh running for 90s
% 121.73/16.25  % Solved by lams/30_b.l.sh.
% 121.73/16.25  % done 467 iterations in 14.879s
% 121.73/16.25  % SZS status Theorem for '/export/starexec/sandbox/benchmark/theBenchmark.p'
% 121.73/16.25  % SZS output start Refutation
% 121.73/16.25  thf(setadjoinAx_type, type, setadjoinAx: $o).
% 121.73/16.25  thf(cartprodfstpairEq_type, type, cartprodfstpairEq: $o).
% 121.73/16.25  thf(notdexE_type, type, notdexE: $o).
% 121.73/16.25  thf(setunionAx_type, type, setunionAx: $o).
% 121.73/16.25  thf(setminusELneg_type, type, setminusELneg: $o).
% 121.73/16.25  thf(breln1unionEcases_type, type, breln1unionEcases: $o).
% 121.73/16.25  thf('#sk16_type', type, '#sk16': $i > $i).
% 121.73/16.25  thf(omegaSp_type, type, omegaSp: $o).
% 121.73/16.25  thf(powersetE_type, type, powersetE: $o).
% 121.73/16.25  thf(woz1_1_type, type, woz1_1: $o).
% 121.73/16.25  thf(omegaSAx_type, type, omegaSAx: $o).
% 121.73/16.25  thf(breln1unionI_type, type, breln1unionI: $o).
% 121.73/16.25  thf(complementSubsetComplementIntersect_type, type, complementSubsetComplementIntersect: 
% 121.73/16.25      $o).
% 121.73/16.25  thf(surjCantorThm_type, type, surjCantorThm: $o).
% 121.73/16.25  thf(exuI1_type, type, exuI1: $o).
% 121.73/16.25  thf(exuI2_type, type, exuI2: $o).
% 121.73/16.25  thf(notequalI2_type, type, notequalI2: $o).
% 121.73/16.25  thf('#form172_type', type, '#form172': $i > $i > $o).
% 121.73/16.25  thf(kfstsingleton_type, type, kfstsingleton: $o).
% 121.73/16.25  thf(kpairiskpair_type, type, kpairiskpair: $o).
% 121.73/16.25  thf(upairsubunion_type, type, upairsubunion: $o).
% 121.73/16.25  thf(binunionTE_type, type, binunionTE: $o).
% 121.73/16.25  thf(binunionTEcontra_type, type, binunionTEcontra: $o).
% 121.73/16.25  thf(powerset__Cong_type, type, powerset__Cong: $o).
% 121.73/16.25  thf(setukpairinjR2_type, type, setukpairinjR2: $o).
% 121.73/16.25  thf(singletonsuniq_type, type, singletonsuniq: $o).
% 121.73/16.25  thf(setminusILneg_type, type, setminusILneg: $o).
% 121.73/16.25  thf(wellorderingAx_type, type, wellorderingAx: $o).
% 121.73/16.25  thf(kpairsurjEq_type, type, kpairsurjEq: $o).
% 121.73/16.25  thf(funcextLem_type, type, funcextLem: $o).
% 121.73/16.25  thf(setadjoinSub2_type, type, setadjoinSub2: $o).
% 121.73/16.25  thf(binintersectSubset5_type, type, binintersectSubset5: $o).
% 121.73/16.25  thf(upairinpowunion_type, type, upairinpowunion: $o).
% 121.73/16.25  thf('#sk111_type', type, '#sk111': $i > $i > $i).
% 121.73/16.25  thf(eta1_type, type, eta1: $o).
% 121.73/16.25  thf(complementTnotintersectT_type, type, complementTnotintersectT: $o).
% 121.73/16.25  thf(setoftrueEq_type, type, setoftrueEq: $o).
% 121.73/16.25  thf(notinself_type, type, notinself: $o).
% 121.73/16.25  thf(apProp_type, type, apProp: $o).
% 121.73/16.25  thf(setextT_type, type, setextT: $o).
% 121.73/16.25  thf(inIntersectImpInIntersectUnions_type, type, inIntersectImpInIntersectUnions: 
% 121.73/16.25      $o).
% 121.73/16.25  thf(emptyset__Cong_type, type, emptyset__Cong: $o).
% 121.73/16.25  thf(cartprodmempaircEq_type, type, cartprodmempaircEq: $o).
% 121.73/16.25  thf(breln1invprop_type, type, breln1invprop: $o).
% 121.73/16.25  thf(lamProp_type, type, lamProp: $o).
% 121.73/16.25  thf(dpsetconstrSub_type, type, dpsetconstrSub: $o).
% 121.73/16.25  thf(setunionTransitive_type, type, setunionTransitive: $o).
% 121.73/16.25  thf(ex1E1_type, type, ex1E1: $o).
% 121.73/16.25  thf(sepInPowerset_type, type, sepInPowerset: $o).
% 121.73/16.25  thf(setukpairIR_type, type, setukpairIR: $o).
% 121.73/16.25  thf(brelnall1_type, type, brelnall1: $o).
% 121.73/16.25  thf(binunionE_type, type, binunionE: $o).
% 121.73/16.25  thf(setext_type, type, setext: $o).
% 121.73/16.25  thf(complementTcontraSubset_type, type, complementTcontraSubset: $o).
% 121.73/16.25  thf(emptyinPowerset_type, type, emptyinPowerset: $o).
% 121.73/16.25  thf(binintersectTELcontra_type, type, binintersectTELcontra: $o).
% 121.73/16.25  thf(ubforcartprodlem1_type, type, ubforcartprodlem1: $o).
% 121.73/16.25  thf(iftrue_type, type, iftrue: $o).
% 121.73/16.25  thf(woz13rule4_type, type, woz13rule4: $o).
% 121.73/16.25  thf(descr__Cong_type, type, descr__Cong: $o).
% 121.73/16.25  thf(funcGraphProp2_type, type, funcGraphProp2: $o).
% 121.73/16.25  thf(theprop_type, type, theprop: $o).
% 121.73/16.25  thf(image1I_type, type, image1I: $o).
% 121.73/16.25  thf(binintersectSubset1_type, type, binintersectSubset1: $o).
% 121.73/16.25  thf(in_type, type, in: $i > $i > $o).
% 121.73/16.25  thf('#sk1597_type', type, '#sk1597': $i).
% 121.73/16.25  thf(cartprodsndpairEq_type, type, cartprodsndpairEq: $o).
% 121.73/16.25  thf(quantDeMorgan1_type, type, quantDeMorgan1: $o).
% 121.73/16.25  thf(setukpairinjL2_type, type, setukpairinjL2: $o).
% 121.73/16.25  thf(demorgan1_type, type, demorgan1: $o).
% 121.73/16.25  thf(setadjoinIR_type, type, setadjoinIR: $o).
% 121.73/16.25  thf(complementInPowersetComplementIntersect_type, type, complementInPowersetComplementIntersect: 
% 121.73/16.25      $o).
% 121.73/16.25  thf(inIntersectImpInUnion_type, type, inIntersectImpInUnion: $o).
% 121.73/16.25  thf(breln1SetBreln1_type, type, breln1SetBreln1: $o).
% 121.73/16.25  thf(setadjoin__Cong_type, type, setadjoin__Cong: $o).
% 121.73/16.25  thf(ksndpairEq_type, type, ksndpairEq: $o).
% 121.73/16.25  thf(ex1I2_type, type, ex1I2: $o).
% 121.73/16.25  thf(foundation2_type, type, foundation2: $o).
% 121.73/16.25  thf(symdiffI2_type, type, symdiffI2: $o).
% 121.77/16.25  thf(ap2apEq2_type, type, ap2apEq2: $o).
% 121.77/16.25  thf(ifSingleton_type, type, ifSingleton: $o).
% 121.77/16.25  thf(upairset2IR_type, type, upairset2IR: $o).
% 121.77/16.25  thf(iftrueProp1_type, type, iftrueProp1: $o).
% 121.77/16.25  thf(complementTI1_type, type, complementTI1: $o).
% 121.77/16.25  thf(subsetE_type, type, subsetE: $o).
% 121.77/16.25  thf(wellorderedByIn_type, type, wellorderedByIn: $i > $o).
% 121.77/16.25  thf(prop2set2propI_type, type, prop2set2propI: $o).
% 121.77/16.25  thf(doubleComplementSub2_type, type, doubleComplementSub2: $o).
% 121.77/16.25  thf(complementUnionInPowersetComplement_type, type, complementUnionInPowersetComplement: 
% 121.77/16.25      $o).
% 121.77/16.25  thf(iffalse_type, type, iffalse: $o).
% 121.77/16.25  thf(dsetconstrEL_type, type, dsetconstrEL: $o).
% 121.77/16.25  thf(setbeta_type, type, setbeta: $o).
% 121.77/16.25  thf(eqinunit_type, type, eqinunit: $o).
% 121.77/16.25  thf(upairsetIL_type, type, upairsetIL: $o).
% 121.77/16.25  thf(powersetI1_type, type, powersetI1: $o).
% 121.77/16.25  thf(cartprodfstin_type, type, cartprodfstin: $o).
% 121.77/16.25  thf(lamp_type, type, lamp: $o).
% 121.77/16.25  thf(iffalseProp1_type, type, iffalseProp1: $o).
% 121.77/16.25  thf(breln1invI_type, type, breln1invI: $o).
% 121.77/16.25  thf('#sk337_type', type, '#sk337': $i > ($i > $o) > $i).
% 121.77/16.25  thf(binintersectSubset3_type, type, binintersectSubset3: $o).
% 121.77/16.25  thf(breln1unionE_type, type, breln1unionE: $o).
% 121.77/16.25  thf(ksndsingleton_type, type, ksndsingleton: $o).
% 121.77/16.25  thf(setminusIRneg_type, type, setminusIRneg: $o).
% 121.77/16.25  thf(lam2lamEq_type, type, lam2lamEq: $o).
% 121.77/16.25  thf(powersetAx_type, type, powersetAx: $o).
% 121.77/16.25  thf(woz2Ex_type, type, woz2Ex: $o).
% 121.77/16.25  thf(eta2_type, type, eta2: $o).
% 121.77/16.25  thf(binintersectSubset4_type, type, binintersectSubset4: $o).
% 121.77/16.25  thf(singletoninpowunion_type, type, singletoninpowunion: $o).
% 121.77/16.25  thf(image1Ex_type, type, image1Ex: $o).
% 121.77/16.25  thf(powersetI_type, type, powersetI: $o).
% 121.77/16.25  thf(cartprodmempair_type, type, cartprodmempair: $o).
% 121.77/16.25  thf(powersetTE1_type, type, powersetTE1: $o).
% 121.77/16.25  thf(upairsetIR_type, type, upairsetIR: $o).
% 121.77/16.25  thf(cartprodpairsurjEq_type, type, cartprodpairsurjEq: $o).
% 121.77/16.25  thf(lam2p_type, type, lam2p: $o).
% 121.77/16.25  thf(contraSubsetComplement_type, type, contraSubsetComplement: $o).
% 121.77/16.25  thf(doubleComplementSub1_type, type, doubleComplementSub1: $o).
% 121.77/16.25  thf(cartprodpairmemEL_type, type, cartprodpairmemEL: $o).
% 121.77/16.25  thf(setOfPairsIsBReln1_type, type, setOfPairsIsBReln1: $o).
% 121.77/16.25  thf(inCongP_type, type, inCongP: $o).
% 121.77/16.25  thf(setukpairinjR11_type, type, setukpairinjR11: $o).
% 121.77/16.25  thf(setadjoinSub_type, type, setadjoinSub: $o).
% 121.77/16.25  thf(exuE3e_type, type, exuE3e: $o).
% 121.77/16.25  thf(emptysetE_type, type, emptysetE: $o).
% 121.77/16.25  thf(woz13rule2_type, type, woz13rule2: $o).
% 121.77/16.25  thf(binintersectSubset2_type, type, binintersectSubset2: $o).
% 121.77/16.25  thf(peano0notS_type, type, peano0notS: $o).
% 121.77/16.25  thf(image1E_type, type, image1E: $o).
% 121.77/16.25  thf(setunionI_type, type, setunionI: $o).
% 121.77/16.25  thf(breln1unionIR_type, type, breln1unionIR: $o).
% 121.77/16.25  thf(binintersectTERcontra_type, type, binintersectTERcontra: $o).
% 121.77/16.25  thf(setunion__Cong_type, type, setunion__Cong: $o).
% 121.77/16.25  thf(injFuncSetFuncInj_type, type, injFuncSetFuncInj: $o).
% 121.77/16.25  thf(prop2setI_type, type, prop2setI: $o).
% 121.77/16.25  thf(nonemptyImpWitness_type, type, nonemptyImpWitness: $o).
% 121.77/16.25  thf(setminusER_type, type, setminusER: $o).
% 121.77/16.25  thf(peanoSinj_type, type, peanoSinj: $o).
% 121.77/16.25  thf(exuE2_type, type, exuE2: $o).
% 121.77/16.25  thf(woz1_2_type, type, woz1_2: $o).
% 121.77/16.25  thf(emptyset_type, type, emptyset: $i).
% 121.77/16.25  thf(setukpairinjR12_type, type, setukpairinjR12: $o).
% 121.77/16.25  thf(funcGraphProp1_type, type, funcGraphProp1: $o).
% 121.77/16.25  thf(setminus_type, type, setminus: $i > $i > $i).
% 121.77/16.25  thf(powersetsubset_type, type, powersetsubset: $o).
% 121.77/16.25  thf(upairequniteq_type, type, upairequniteq: $o).
% 121.77/16.25  thf(dpsetconstrEL1_type, type, dpsetconstrEL1: $o).
% 121.77/16.25  thf(ordinal_type, type, ordinal: $i > $o).
% 121.77/16.25  thf(injFuncInInjFuncSet_type, type, injFuncInInjFuncSet: $o).
% 121.77/16.25  thf(subPowSU_type, type, subPowSU: $o).
% 121.77/16.25  thf('#form1598_type', type, '#form1598': $i > $o).
% 121.77/16.25  thf(breln1compprop_type, type, breln1compprop: $o).
% 121.77/16.25  thf(woz2B_type, type, woz2B: $o).
% 121.77/16.25  thf(notequalI1_type, type, notequalI1: $o).
% 121.77/16.25  thf(demorgan2b_type, type, demorgan2b: $o).
% 121.77/16.25  thf(notinemptyset_type, type, notinemptyset: $o).
% 121.77/16.25  thf(nonemptyI1_type, type, nonemptyI1: $o).
% 121.77/16.25  thf(breln1unionIL_type, type, breln1unionIL: $o).
% 121.77/16.25  thf(subsetTrans_type, type, subsetTrans: $o).
% 121.77/16.25  thf(setukpairinjR_type, type, setukpairinjR: $o).
% 121.77/16.25  thf(infuncsetfunc_type, type, infuncsetfunc: $o).
% 121.77/16.25  thf(kpairp_type, type, kpairp: $o).
% 121.77/16.25  thf(setukpairinjR1_type, type, setukpairinjR1: $o).
% 121.77/16.25  thf(setminusI_type, type, setminusI: $o).
% 121.77/16.25  thf(notinself2_type, type, notinself2: $o).
% 121.77/16.25  thf(binunionIL_type, type, binunionIL: $o).
% 121.77/16.25  thf(setOfPairsIsBReln_type, type, setOfPairsIsBReln: $o).
% 121.77/16.25  thf(setukpairinjL1_type, type, setukpairinjL1: $o).
% 121.77/16.25  thf(setunionsingleton_type, type, setunionsingleton: $o).
% 121.77/16.25  thf(powersetTI1_type, type, powersetTI1: $o).
% 121.77/16.25  thf(subsetE2_type, type, subsetE2: $o).
% 121.77/16.25  thf(image1Ex1_type, type, image1Ex1: $o).
% 121.77/16.25  thf(singletonsswitch_type, type, singletonsswitch: $o).
% 121.77/16.25  thf(ubforcartprodlem3_type, type, ubforcartprodlem3: $o).
% 121.77/16.25  thf(setextsub_type, type, setextsub: $o).
% 121.77/16.25  thf(binunionLsub_type, type, binunionLsub: $o).
% 121.77/16.25  thf(contrasubsetT1_type, type, contrasubsetT1: $o).
% 121.77/16.25  thf(setunionsingleton1_type, type, setunionsingleton1: $o).
% 121.77/16.25  thf(breln1compE_type, type, breln1compE: $o).
% 121.77/16.25  thf(binintersect_type, type, binintersect: $i > $i > $i).
% 121.77/16.25  thf(emptysetsubset_type, type, emptysetsubset: $o).
% 121.77/16.25  thf(quantDeMorgan3_type, type, quantDeMorgan3: $o).
% 121.77/16.25  thf(dpsetconstrERa_type, type, dpsetconstrERa: $o).
% 121.77/16.25  thf(setunionE_type, type, setunionE: $o).
% 121.77/16.25  thf(setminusSubset1_type, type, setminusSubset1: $o).
% 121.77/16.25  thf(complementT_lem_type, type, complementT_lem: $o).
% 121.77/16.25  thf(binintersectT_lem_type, type, binintersectT_lem: $o).
% 121.77/16.25  thf(emptyinunitempty_type, type, emptyinunitempty: $o).
% 121.77/16.25  thf(binunionIR_type, type, binunionIR: $o).
% 121.77/16.25  thf(injFuncSetFuncIn_type, type, injFuncSetFuncIn: $o).
% 121.77/16.25  thf(setadjoinE_type, type, setadjoinE: $o).
% 121.77/16.25  thf(doubleComplementEq_type, type, doubleComplementEq: $o).
% 121.77/16.25  thf(eqbreln1_type, type, eqbreln1: $o).
% 121.77/16.25  thf(cartprodpairmemER_type, type, cartprodpairmemER: $o).
% 121.77/16.25  thf(dpsetconstrER_type, type, dpsetconstrER: $o).
% 121.77/16.25  thf(leftInvIsSurj_type, type, leftInvIsSurj: $o).
% 121.77/16.25  thf(doubleComplementE1_type, type, doubleComplementE1: $o).
% 121.77/16.25  thf(setadjoinIL_type, type, setadjoinIL: $o).
% 121.77/16.25  thf(exuE1_type, type, exuE1: $o).
% 121.77/16.25  thf(ubforcartprodlem2_type, type, ubforcartprodlem2: $o).
% 121.77/16.25  thf(binintersectRsub_type, type, binintersectRsub: $o).
% 121.77/16.25  thf(setminusLsub_type, type, setminusLsub: $o).
% 121.77/16.25  thf(notinsingleton_type, type, notinsingleton: $o).
% 121.77/16.25  thf(intersectInPowersetIntersectUnions_type, type, intersectInPowersetIntersectUnions: 
% 121.77/16.25      $o).
% 121.77/16.25  thf(dpsetconstrEL2_type, type, dpsetconstrEL2: $o).
% 121.77/16.25  thf(eqimpsubset2_type, type, eqimpsubset2: $o).
% 121.77/16.25  thf(exuEu_type, type, exuEu: $o).
% 121.77/16.25  thf(emptysetimpfalse_type, type, emptysetimpfalse: $o).
% 121.77/16.25  thf(upairsetE_type, type, upairsetE: $o).
% 121.77/16.25  thf(omega0Ax_type, type, omega0Ax: $o).
% 121.77/16.25  thf(breln1invE_type, type, breln1invE: $o).
% 121.77/16.25  thf(breln1unionCommutes_type, type, breln1unionCommutes: $o).
% 121.77/16.25  thf(funcGraphProp3_type, type, funcGraphProp3: $o).
% 121.77/16.25  thf(app_type, type, app: $o).
% 121.77/16.25  thf(transitiveset_type, type, transitiveset: $i > $o).
% 121.77/16.25  thf(funcImageSingleton_type, type, funcImageSingleton: $o).
% 121.77/16.25  thf(dpsetconstrI_type, type, dpsetconstrI: $o).
% 121.77/16.25  thf(notsubsetI_type, type, notsubsetI: $o).
% 121.77/16.25  thf(powersetT_lem_type, type, powersetT_lem: $o).
% 121.77/16.25  thf(binintTransitive_type, type, binintTransitive: $o).
% 121.77/16.25  thf(woz2W_type, type, woz2W: $o).
% 121.77/16.25  thf(iffalseProp2_type, type, iffalseProp2: $o).
% 121.77/16.25  thf(quantDeMorgan4_type, type, quantDeMorgan4: $o).
% 121.77/16.25  thf(setextAx_type, type, setextAx: $o).
% 121.77/16.25  thf(breln1all1_type, type, breln1all1: $o).
% 121.77/16.25  thf(choice2fnsingleton_type, type, choice2fnsingleton: $o).
% 121.77/16.25  thf(breln1compI_type, type, breln1compI: $o).
% 121.77/16.25  thf(demorgan2a1_type, type, demorgan2a1: $o).
% 121.77/16.25  thf(powersetE1_type, type, powersetE1: $o).
% 121.77/16.25  thf(bs114d_type, type, bs114d: $o).
% 121.77/16.25  thf(complementTE1_type, type, complementTE1: $o).
% 121.77/16.25  thf(noeltsimpempty_type, type, noeltsimpempty: $o).
% 121.77/16.25  thf(breln1all2_type, type, breln1all2: $o).
% 121.77/16.25  thf(contrasubsetT2_type, type, contrasubsetT2: $o).
% 121.77/16.25  thf(inIntersectImpInUnion2_type, type, inIntersectImpInUnion2: $o).
% 121.77/16.25  thf(demorgan2b2_type, type, demorgan2b2: $o).
% 121.77/16.25  thf('#sk134_type', type, '#sk134': $i > $i > $i).
% 121.77/16.25  thf(binintersectLsub_type, type, binintersectLsub: $o).
% 121.77/16.25  thf(subsetI1_type, type, subsetI1: $o).
% 121.77/16.25  thf(symdiffE_type, type, symdiffE: $o).
% 121.77/16.25  thf(woz13rule1_type, type, woz13rule1: $o).
% 121.77/16.25  thf(breln1unionprop_type, type, breln1unionprop: $o).
% 121.77/16.25  thf(descrp_type, type, descrp: $o).
% 121.77/16.25  thf(dsetconstr__Cong_type, type, dsetconstr__Cong: $o).
% 121.77/16.25  thf(foundationAx_type, type, foundationAx: $o).
% 121.77/16.25  thf(brelnall2_type, type, brelnall2: $o).
% 121.77/16.25  thf(emptysetAx_type, type, emptysetAx: $o).
% 121.77/16.25  thf(emptyI_type, type, emptyI: $o).
% 121.77/16.25  thf(setadjoinOr_type, type, setadjoinOr: $o).
% 121.77/16.25  thf(binintersectEL_type, type, binintersectEL: $o).
% 121.77/16.25  thf(emptyE1_type, type, emptyE1: $o).
% 121.77/16.25  thf(demorgan2a_type, type, demorgan2a: $o).
% 121.77/16.25  thf(woz1_3_type, type, woz1_3: $o).
% 121.77/16.25  thf(emptyInPowerset_type, type, emptyInPowerset: $o).
% 121.77/16.25  thf(vacuousDall_type, type, vacuousDall: $o).
% 121.77/16.25  thf(dsetconstrER_type, type, dsetconstrER: $o).
% 121.77/16.25  thf(demorgan1a_type, type, demorgan1a: $o).
% 121.77/16.25  thf(ifp_type, type, ifp: $o).
% 121.77/16.25  thf(binintersectI_type, type, binintersectI: $o).
% 121.77/16.25  thf(beta1_type, type, beta1: $o).
% 121.77/16.25  thf(funcext2_type, type, funcext2: $o).
% 121.77/16.25  thf(subbreln_type, type, subbreln: $o).
% 121.77/16.25  thf(cartprodpairin_type, type, cartprodpairin: $o).
% 121.77/16.25  thf(ordinalMinLem1_type, type, ordinalMinLem1: $o).
% 121.77/16.25  thf(cartprodmempair1_type, type, cartprodmempair1: $o).
% 121.77/16.25  thf(subbreln1_type, type, subbreln1: $o).
% 121.77/16.25  thf(demorgan2a2_type, type, demorgan2a2: $o).
% 121.77/16.25  thf(image1Equiv_type, type, image1Equiv: $o).
% 121.77/16.25  thf(subsetTI_type, type, subsetTI: $o).
% 121.77/16.25  thf(setminusT_lem_type, type, setminusT_lem: $o).
% 121.77/16.25  thf(ap2p_type, type, ap2p: $o).
% 121.77/16.25  thf(doubleComplementI1_type, type, doubleComplementI1: $o).
% 121.77/16.25  thf(binunionT_lem_type, type, binunionT_lem: $o).
% 121.77/16.25  thf(symdiffI1_type, type, symdiffI1: $o).
% 121.77/16.25  thf(woz1_4_type, type, woz1_4: $o).
% 121.77/16.25  thf(kfstpairEq_type, type, kfstpairEq: $o).
% 121.77/16.25  thf(subsetI2_type, type, subsetI2: $o).
% 121.77/16.25  thf(symdiffIneg1_type, type, symdiffIneg1: $o).
% 121.77/16.25  thf('#sk1599_type', type, '#sk1599': $i).
% 121.77/16.25  thf(theeq_type, type, theeq: $o).
% 121.77/16.25  thf(setminusERneg_type, type, setminusERneg: $o).
% 121.77/16.25  thf(symdiffIneg2_type, type, symdiffIneg2: $o).
% 121.77/16.25  thf(binunionTIRcontra_type, type, binunionTIRcontra: $o).
% 121.77/16.25  thf(omega__Cong_type, type, omega__Cong: $o).
% 121.77/16.25  thf(demorgan1b_type, type, demorgan1b: $o).
% 121.77/16.25  thf(subsetRefl_type, type, subsetRefl: $o).
% 121.77/16.25  thf(uniqinunit_type, type, uniqinunit: $o).
% 121.77/16.25  thf(eqbreln_type, type, eqbreln: $o).
% 121.77/16.25  thf(inComplementUnionImpNotIn1_type, type, inComplementUnionImpNotIn1: $o).
% 121.77/16.25  thf(funcinfuncset_type, type, funcinfuncset: $o).
% 121.77/16.25  thf(breln1compEex_type, type, breln1compEex: $o).
% 121.77/16.25  thf(contrasubsetT_type, type, contrasubsetT: $o).
% 121.77/16.25  thf(setminusSubset2_type, type, setminusSubset2: $o).
% 121.77/16.25  thf(prop2setE_type, type, prop2setE: $o).
% 121.77/16.25  thf(omegaSclos_type, type, omegaSclos: $o).
% 121.77/16.25  thf(binunionEcases_type, type, binunionEcases: $o).
% 121.77/16.25  thf(omega_type, type, omega: $i).
% 121.77/16.25  thf('#sk1600_type', type, '#sk1600': $i).
% 121.77/16.25  thf(nonemptyI_type, type, nonemptyI: $o).
% 121.77/16.25  thf(disjointsetsI1_type, type, disjointsetsI1: $o).
% 121.77/16.25  thf(woz2A_type, type, woz2A: $o).
% 121.77/16.25  thf(transitivesetOp1_type, type, transitivesetOp1: $o).
% 121.77/16.25  thf(exuE3u_type, type, exuE3u: $o).
% 121.77/16.25  thf(setminusEL_type, type, setminusEL: $o).
% 121.77/16.25  thf(funcGraphProp4_type, type, funcGraphProp4: $o).
% 121.77/16.25  thf(woz1_5_type, type, woz1_5: $o).
% 121.77/16.25  thf(demorgan2_type, type, demorgan2: $o).
% 121.77/16.25  thf(setunionsingleton2_type, type, setunionsingleton2: $o).
% 121.77/16.25  thf(sepSubset_type, type, sepSubset: $o).
% 121.77/16.25  thf(inComplementUnionImpInComplement1_type, type, inComplementUnionImpInComplement1: 
% 121.77/16.25      $o).
% 121.77/16.25  thf(transitivesetOp2_type, type, transitivesetOp2: $o).
% 121.77/16.25  thf(funcext_type, type, funcext: $o).
% 121.77/16.25  thf(surjFuncSetFuncSurj_type, type, surjFuncSetFuncSurj: $o).
% 121.77/16.25  thf(upairset2E_type, type, upairset2E: $o).
% 121.77/16.25  thf(eqimpsubset1_type, type, eqimpsubset1: $o).
% 121.77/16.25  thf(exuI3_type, type, exuI3: $o).
% 121.77/16.25  thf(notdallE_type, type, notdallE: $o).
% 121.77/16.25  thf(iftrueProp2_type, type, iftrueProp2: $o).
% 121.77/16.25  thf(binintersectER_type, type, binintersectER: $o).
% 121.77/16.25  thf(powerset_type, type, powerset: $i > $i).
% 121.77/16.25  thf(woz13rule0_type, type, woz13rule0: $o).
% 121.77/16.25  thf(dsetconstrI_type, type, dsetconstrI: $o).
% 121.77/16.25  thf(beta2_type, type, beta2: $o).
% 121.77/16.25  thf(setadjoin_type, type, setadjoin: $i > $i > $i).
% 121.77/16.25  thf(exu__Cong_type, type, exu__Cong: $o).
% 121.77/16.25  thf(cartprodsndin_type, type, cartprodsndin: $o).
% 121.77/16.25  thf(iftrueorfalse_type, type, iftrueorfalse: $o).
% 121.77/16.25  thf(surjFuncSetFuncIn_type, type, surjFuncSetFuncIn: $o).
% 121.77/16.25  thf(quantDeMorgan2_type, type, quantDeMorgan2: $o).
% 121.77/16.25  thf(ex1I_type, type, ex1I: $o).
% 121.77/16.25  thf(secondinupair_type, type, secondinupair: $o).
% 121.77/16.25  thf(singletonprop_type, type, singletonprop: $o).
% 121.77/16.25  thf(singletonsubset_type, type, singletonsubset: $o).
% 121.77/16.25  thf(singletoninpowerset_type, type, singletoninpowerset: $o).
% 121.77/16.25  thf(subsetemptysetimpeq_type, type, subsetemptysetimpeq: $o).
% 121.77/16.25  thf(ex1E2_type, type, ex1E2: $o).
% 121.77/16.25  thf(replAx_type, type, replAx: $o).
% 121.77/16.25  thf(nonemptyE1_type, type, nonemptyE1: $o).
% 121.77/16.25  thf(omegaIndAx_type, type, omegaIndAx: $o).
% 121.77/16.25  thf(setukpairIL_type, type, setukpairIL: $o).
% 121.77/16.25  thf(setunionE2_type, type, setunionE2: $o).
% 121.77/16.25  thf(inPowerset_type, type, inPowerset: $o).
% 121.77/16.25  thf(binunionTILcontra_type, type, binunionTILcontra: $o).
% 121.77/16.25  thf(ap2apEq1_type, type, ap2apEq1: $o).
% 121.77/16.25  thf(contrasubsetT3_type, type, contrasubsetT3: $o).
% 121.77/16.25  thf(subset_type, type, subset: $i > $i > $o).
% 121.77/16.25  thf(woz13rule3_type, type, woz13rule3: $o).
% 121.77/16.25  thf(complementImpComplementIntersect_type, type, complementImpComplementIntersect: 
% 121.77/16.25      $o).
% 121.77/16.25  thf(in__Cong_type, type, in__Cong: $o).
% 121.77/16.25  thf(setukpairinjL_type, type, setukpairinjL: $o).
% 121.77/16.25  thf(binunionRsub_type, type, binunionRsub: $o).
% 121.77/16.25  thf(subset2powerset_type, type, subset2powerset: $o).
% 121.77/16.25  thf(ordinalTransSet, conjecture,
% 121.77/16.25    (( setextAx ) =>
% 121.77/16.25     ( ( emptysetAx ) =>
% 121.77/16.25       ( ( setadjoinAx ) =>
% 121.77/16.25         ( ( powersetAx ) =>
% 121.77/16.25           ( ( setunionAx ) =>
% 121.77/16.25             ( ( omega0Ax ) =>
% 121.77/16.25               ( ( omegaSAx ) =>
% 121.77/16.25                 ( ( omegaIndAx ) =>
% 121.77/16.25                   ( ( replAx ) =>
% 121.77/16.25                     ( ( foundationAx ) =>
% 121.77/16.25                       ( ( wellorderingAx ) =>
% 121.77/16.25                         ( ( descrp ) =>
% 121.77/16.25                           ( ( dsetconstrI ) =>
% 121.77/16.25                             ( ( dsetconstrEL ) =>
% 121.77/16.25                               ( ( dsetconstrER ) =>
% 121.77/16.25                                 ( ( exuE1 ) =>
% 121.77/16.25                                   ( ( prop2setE ) =>
% 121.77/16.25                                     ( ( emptysetE ) =>
% 121.77/16.25                                       ( ( emptysetimpfalse ) =>
% 121.77/16.25                                         ( ( notinemptyset ) =>
% 121.77/16.25                                           ( ( exuE3e ) =>
% 121.77/16.25                                             ( ( setext ) =>
% 121.77/16.25                                               ( ( emptyI ) =>
% 121.77/16.25                                                 ( ( noeltsimpempty ) =>
% 121.77/16.25                                                   ( ( setbeta ) =>
% 121.77/16.25                                                     ( ( nonemptyE1 ) =>
% 121.77/16.25                                                       ( ( nonemptyI ) =>
% 121.77/16.25                                                         ( ( nonemptyI1 ) =>
% 121.77/16.25                                                           ( ( setadjoinIL ) =>
% 121.77/16.25                                                             ( ( emptyinunitempty ) =>
% 121.77/16.25                                                               ( ( setadjoinIR ) =>
% 121.77/16.25                                                                 ( ( setadjoinE ) =>
% 121.77/16.25                                                                   ( ( 
% 121.77/16.25                                                                     setadjoinOr ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setoftrueEq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     powersetI ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     emptyinPowerset ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     emptyInPowerset ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     powersetE ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setunionI ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setunionE ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     subPowSU ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     exuE2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     nonemptyImpWitness ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     uniqinunit ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     notinsingleton ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     eqinunit ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     singletonsswitch ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     upairsetE ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     upairsetIL ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     upairsetIR ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     emptyE1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     vacuousDall ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     quantDeMorgan1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     quantDeMorgan2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     quantDeMorgan3 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     quantDeMorgan4 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     prop2setI ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     prop2set2propI ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     notdexE ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     notdallE ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     exuI1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     exuI3 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     exuI2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     inCongP ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     in__Cong ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     exuE3u ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     exu__Cong ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     emptyset__Cong ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setadjoin__Cong ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     powerset__Cong ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setunion__Cong ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     omega__Cong ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     exuEu ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     descr__Cong ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     dsetconstr__Cong ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     subsetI1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     eqimpsubset2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     eqimpsubset1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     subsetI2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     emptysetsubset ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     subsetE ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     subsetE2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     notsubsetI ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     notequalI1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     notequalI2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     subsetRefl ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     subsetTrans ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setadjoinSub ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setadjoinSub2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     subset2powerset ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setextsub ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     subsetemptysetimpeq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     powersetI1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     powersetE1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     inPowerset ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     powersetsubset ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     sepInPowerset ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     sepSubset ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binunionIL ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     upairset2IR ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binunionIR ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binunionEcases ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binunionE ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binunionLsub ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binunionRsub ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectI ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectSubset5 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectEL ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectLsub ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectSubset2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectSubset3 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectER ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     disjointsetsI1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectRsub ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectSubset4 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectSubset1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     bs114d ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setminusI ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setminusEL ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setminusER ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setminusSubset2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setminusERneg ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setminusELneg ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setminusILneg ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setminusIRneg ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setminusLsub ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setminusSubset1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     symdiffE ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     symdiffI1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     symdiffI2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     symdiffIneg1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     symdiffIneg2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     secondinupair ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setukpairIL ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setukpairIR ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     kpairiskpair ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     kpairp ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     singletonsubset ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     singletoninpowerset ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     singletoninpowunion ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     upairset2E ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     upairsubunion ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     upairinpowunion ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ubforcartprodlem1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ubforcartprodlem2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ubforcartprodlem3 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     cartprodpairin ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     cartprodmempair1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     cartprodmempair ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setunionE2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setunionsingleton1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setunionsingleton2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setunionsingleton ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     singletonprop ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ex1E1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ex1I ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ex1I2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     singletonsuniq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setukpairinjL1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     kfstsingleton ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     theprop ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     kfstpairEq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     cartprodfstin ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setukpairinjL2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setukpairinjL ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setukpairinjR11 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setukpairinjR12 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setukpairinjR1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     upairequniteq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setukpairinjR2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setukpairinjR ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ksndsingleton ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ksndpairEq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     kpairsurjEq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     cartprodsndin ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     cartprodpairmemEL ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     cartprodpairmemER ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     cartprodmempaircEq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     cartprodfstpairEq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     cartprodsndpairEq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     cartprodpairsurjEq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     dpsetconstrI ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     dpsetconstrSub ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setOfPairsIsBReln ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     dpsetconstrERa ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     dpsetconstrEL1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     dpsetconstrEL2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     dpsetconstrER ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     funcImageSingleton ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     apProp ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     app ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     infuncsetfunc ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ap2p ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     funcinfuncset ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     lamProp ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     lamp ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     lam2p ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     brelnall1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     brelnall2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ex1E2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     funcGraphProp1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     funcGraphProp3 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     funcGraphProp2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     funcextLem ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     funcGraphProp4 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     subbreln ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     eqbreln ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     funcext ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     funcext2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ap2apEq1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ap2apEq2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     beta1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     eta1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     lam2lamEq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     beta2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     eta2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     iffalseProp1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     iffalseProp2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     iftrueProp1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     iftrueProp2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ifSingleton ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ifp ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     theeq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     iftrue ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     iffalse ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     iftrueorfalse ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectT_lem ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binunionT_lem ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     powersetT_lem ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setminusT_lem ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     complementT_lem ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setextT ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     subsetTI ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     powersetTI1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     powersetTE1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     complementTI1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     complementTE1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectTELcontra ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintersectTERcontra ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     contrasubsetT ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     contrasubsetT1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     contrasubsetT2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     contrasubsetT3 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     doubleComplementI1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     doubleComplementE1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     doubleComplementSub1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     doubleComplementSub2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     doubleComplementEq ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     complementTnotintersectT ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     complementImpComplementIntersect ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     complementSubsetComplementIntersect ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     complementInPowersetComplementIntersect ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     contraSubsetComplement ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     complementTcontraSubset ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binunionTILcontra ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binunionTIRcontra ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     inIntersectImpInUnion ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     inIntersectImpInUnion2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     inIntersectImpInIntersectUnions ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     intersectInPowersetIntersectUnions ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     inComplementUnionImpNotIn1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     inComplementUnionImpInComplement1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binunionTE ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binunionTEcontra ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     demorgan2a1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     complementUnionInPowersetComplement ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     demorgan2a2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     demorgan1a ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     demorgan1b ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     demorgan1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     demorgan2a ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     demorgan2b2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     demorgan2b ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     demorgan2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz13rule0 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz13rule1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz13rule2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz13rule3 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz13rule4 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz1_1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz1_2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz1_3 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz1_4 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz1_5 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1all2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1SetBreln1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     choice2fnsingleton ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setOfPairsIsBReln1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1all1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     subbreln1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     eqbreln1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1invprop ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1invI ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1invE ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1compprop ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1compI ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1compE ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1compEex ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1unionprop ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1unionIL ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1unionIR ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1unionI ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1unionE ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1unionEcases ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     breln1unionCommutes ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz2Ex ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz2W ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz2A ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     woz2B ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     image1Ex ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     image1Ex1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     image1Equiv ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     image1E ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     image1I ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     injFuncInInjFuncSet ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     injFuncSetFuncIn ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     injFuncSetFuncInj ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     surjFuncSetFuncIn ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     surjFuncSetFuncSurj ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     leftInvIsSurj ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     surjCantorThm ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     foundation2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     notinself ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     notinself2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     omegaSp ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     omegaSclos ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     peano0notS ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     peanoSinj ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     transitivesetOp1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     binintTransitive ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     transitivesetOp2 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     setunionTransitive ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ordinalMinLem1 ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ![
% 121.77/16.25                                                                     X:$i]:
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ordinal @
% 121.77/16.25                                                                     X ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ![
% 121.77/16.25                                                                     Xx:$i,A:$i]:
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     in @ A @ X ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     in @
% 121.77/16.25                                                                     Xx @ A ) =>
% 121.77/16.25                                                                     ( 
% 121.77/16.25                                                                     in @
% 121.77/16.25                                                                     Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ))).
% 121.77/16.25  thf(zf_stmt_0, negated_conjecture,
% 121.77/16.25    (~( ( setextAx ) =>
% 121.77/16.25        ( ( emptysetAx ) =>
% 121.77/16.25          ( ( setadjoinAx ) =>
% 121.77/16.25            ( ( powersetAx ) =>
% 121.77/16.25              ( ( setunionAx ) =>
% 121.77/16.25                ( ( omega0Ax ) =>
% 121.77/16.25                  ( ( omegaSAx ) =>
% 121.77/16.25                    ( ( omegaIndAx ) =>
% 121.77/16.25                      ( ( replAx ) =>
% 121.77/16.25                        ( ( foundationAx ) =>
% 121.77/16.25                          ( ( wellorderingAx ) =>
% 121.77/16.25                            ( ( descrp ) =>
% 121.77/16.25                              ( ( dsetconstrI ) =>
% 121.77/16.25                                ( ( dsetconstrEL ) =>
% 121.77/16.25                                  ( ( dsetconstrER ) =>
% 121.77/16.25                                    ( ( exuE1 ) =>
% 121.77/16.25                                      ( ( prop2setE ) =>
% 121.77/16.25                                        ( ( emptysetE ) =>
% 121.77/16.25                                          ( ( emptysetimpfalse ) =>
% 121.77/16.25                                            ( ( notinemptyset ) =>
% 121.77/16.25                                              ( ( exuE3e ) =>
% 121.77/16.25                                                ( ( setext ) =>
% 121.77/16.25                                                  ( ( emptyI ) =>
% 121.77/16.25                                                    ( ( noeltsimpempty ) =>
% 121.77/16.25                                                      ( ( setbeta ) =>
% 121.77/16.25                                                        ( ( nonemptyE1 ) =>
% 121.77/16.25                                                          ( ( nonemptyI ) =>
% 121.77/16.25                                                            ( ( nonemptyI1 ) =>
% 121.77/16.25                                                              ( ( setadjoinIL ) =>
% 121.77/16.25                                                                ( ( emptyinunitempty ) =>
% 121.77/16.25                                                                  ( ( setadjoinIR ) =>
% 121.77/16.25                                                                    ( ( 
% 121.77/16.25                                                                      setadjoinE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setadjoinOr ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setoftrueEq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      powersetI ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      emptyinPowerset ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      emptyInPowerset ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      powersetE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setunionI ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setunionE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      subPowSU ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      exuE2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      nonemptyImpWitness ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      uniqinunit ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      notinsingleton ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      eqinunit ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      singletonsswitch ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      upairsetE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      upairsetIL ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      upairsetIR ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      emptyE1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      vacuousDall ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      quantDeMorgan1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      quantDeMorgan2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      quantDeMorgan3 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      quantDeMorgan4 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      prop2setI ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      prop2set2propI ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      notdexE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      notdallE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      exuI1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      exuI3 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      exuI2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      inCongP ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      in__Cong ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      exuE3u ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      exu__Cong ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      emptyset__Cong ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setadjoin__Cong ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      powerset__Cong ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setunion__Cong ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      omega__Cong ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      exuEu ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      descr__Cong ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      dsetconstr__Cong ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      subsetI1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      eqimpsubset2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      eqimpsubset1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      subsetI2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      emptysetsubset ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      subsetE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      subsetE2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      notsubsetI ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      notequalI1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      notequalI2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      subsetRefl ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      subsetTrans ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setadjoinSub ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setadjoinSub2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      subset2powerset ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setextsub ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      subsetemptysetimpeq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      powersetI1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      powersetE1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      inPowerset ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      powersetsubset ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      sepInPowerset ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      sepSubset ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binunionIL ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      upairset2IR ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binunionIR ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binunionEcases ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binunionE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binunionLsub ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binunionRsub ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectI ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectSubset5 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectEL ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectLsub ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectSubset2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectSubset3 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectER ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      disjointsetsI1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectRsub ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectSubset4 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectSubset1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      bs114d ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setminusI ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setminusEL ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setminusER ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setminusSubset2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setminusERneg ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setminusELneg ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setminusILneg ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setminusIRneg ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setminusLsub ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setminusSubset1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      symdiffE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      symdiffI1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      symdiffI2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      symdiffIneg1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      symdiffIneg2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      secondinupair ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setukpairIL ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setukpairIR ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      kpairiskpair ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      kpairp ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      singletonsubset ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      singletoninpowerset ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      singletoninpowunion ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      upairset2E ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      upairsubunion ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      upairinpowunion ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ubforcartprodlem1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ubforcartprodlem2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ubforcartprodlem3 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      cartprodpairin ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      cartprodmempair1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      cartprodmempair ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setunionE2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setunionsingleton1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setunionsingleton2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setunionsingleton ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      singletonprop ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ex1E1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ex1I ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ex1I2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      singletonsuniq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setukpairinjL1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      kfstsingleton ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      theprop ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      kfstpairEq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      cartprodfstin ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setukpairinjL2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setukpairinjL ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setukpairinjR11 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setukpairinjR12 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setukpairinjR1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      upairequniteq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setukpairinjR2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setukpairinjR ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ksndsingleton ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ksndpairEq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      kpairsurjEq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      cartprodsndin ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      cartprodpairmemEL ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      cartprodpairmemER ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      cartprodmempaircEq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      cartprodfstpairEq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      cartprodsndpairEq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      cartprodpairsurjEq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      dpsetconstrI ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      dpsetconstrSub ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setOfPairsIsBReln ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      dpsetconstrERa ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      dpsetconstrEL1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      dpsetconstrEL2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      dpsetconstrER ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      funcImageSingleton ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      apProp ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      app ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      infuncsetfunc ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ap2p ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      funcinfuncset ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      lamProp ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      lamp ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      lam2p ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      brelnall1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      brelnall2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ex1E2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      funcGraphProp1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      funcGraphProp3 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      funcGraphProp2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      funcextLem ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      funcGraphProp4 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      subbreln ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      eqbreln ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      funcext ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      funcext2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ap2apEq1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ap2apEq2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      beta1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      eta1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      lam2lamEq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      beta2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      eta2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      iffalseProp1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      iffalseProp2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      iftrueProp1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      iftrueProp2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ifSingleton ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ifp ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      theeq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      iftrue ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      iffalse ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      iftrueorfalse ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectT_lem ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binunionT_lem ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      powersetT_lem ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setminusT_lem ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      complementT_lem ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setextT ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      subsetTI ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      powersetTI1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      powersetTE1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      complementTI1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      complementTE1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectTELcontra ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintersectTERcontra ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      contrasubsetT ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      contrasubsetT1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      contrasubsetT2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      contrasubsetT3 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      doubleComplementI1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      doubleComplementE1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      doubleComplementSub1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      doubleComplementSub2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      doubleComplementEq ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      complementTnotintersectT ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      complementImpComplementIntersect ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      complementSubsetComplementIntersect ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      complementInPowersetComplementIntersect ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      contraSubsetComplement ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      complementTcontraSubset ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binunionTILcontra ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binunionTIRcontra ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      inIntersectImpInUnion ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      inIntersectImpInUnion2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      inIntersectImpInIntersectUnions ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      intersectInPowersetIntersectUnions ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      inComplementUnionImpNotIn1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      inComplementUnionImpInComplement1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binunionTE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binunionTEcontra ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      demorgan2a1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      complementUnionInPowersetComplement ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      demorgan2a2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      demorgan1a ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      demorgan1b ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      demorgan1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      demorgan2a ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      demorgan2b2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      demorgan2b ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      demorgan2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz13rule0 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz13rule1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz13rule2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz13rule3 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz13rule4 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz1_1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz1_2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz1_3 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz1_4 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz1_5 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1all2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1SetBreln1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      choice2fnsingleton ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setOfPairsIsBReln1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1all1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      subbreln1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      eqbreln1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1invprop ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1invI ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1invE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1compprop ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1compI ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1compE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1compEex ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1unionprop ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1unionIL ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1unionIR ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1unionI ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1unionE ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1unionEcases ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      breln1unionCommutes ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz2Ex ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz2W ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz2A ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      woz2B ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      image1Ex ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      image1Ex1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      image1Equiv ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      image1E ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      image1I ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      injFuncInInjFuncSet ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      injFuncSetFuncIn ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      injFuncSetFuncInj ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      surjFuncSetFuncIn ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      surjFuncSetFuncSurj ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      leftInvIsSurj ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      surjCantorThm ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      foundation2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      notinself ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      notinself2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      omegaSp ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      omegaSclos ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      peano0notS ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      peanoSinj ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      transitivesetOp1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      binintTransitive ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      transitivesetOp2 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      setunionTransitive ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ordinalMinLem1 ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ![
% 121.77/16.25                                                                      X:$i]:
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ordinal @
% 121.77/16.25                                                                      X ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ![
% 121.77/16.25                                                                      Xx:$i,
% 121.77/16.25                                                                      A:$i]:
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      in @
% 121.77/16.25                                                                      A @ X ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      in @
% 121.77/16.25                                                                      Xx @ A ) =>
% 121.77/16.25                                                                      ( 
% 121.77/16.25                                                                      in @
% 121.77/16.25                                                                      Xx @ X ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )),
% 121.77/16.25    inference('cnf.neg', [status(esa)], [ordinalTransSet])).
% 121.77/16.25  thf(zip_derived_cl0, plain,
% 121.77/16.25      (~ (((setextAx) =>
% 121.77/16.25           (((emptysetAx) =>
% 121.77/16.25             (((setadjoinAx) =>
% 121.77/16.25               (((powersetAx) =>
% 121.77/16.25                 (((setunionAx) =>
% 121.77/16.25                   (((omega0Ax) =>
% 121.77/16.25                     (((omegaSAx) =>
% 121.77/16.25                       (((omegaIndAx) =>
% 121.77/16.25                         (((replAx) =>
% 121.77/16.25                           (((foundationAx) =>
% 121.77/16.25                             (((wellorderingAx) =>
% 121.77/16.25                               (((descrp) =>
% 121.77/16.25                                 (((dsetconstrI) =>
% 121.77/16.25                                   (((dsetconstrEL) =>
% 121.77/16.25                                     (((dsetconstrER) =>
% 121.77/16.25                                       (((exuE1) =>
% 121.77/16.25                                         (((prop2setE) =>
% 121.77/16.25                                           (((emptysetE) =>
% 121.77/16.25                                             (((emptysetimpfalse) =>
% 121.77/16.25                                               (((notinemptyset) =>
% 121.77/16.25                                                 (((exuE3e) =>
% 121.77/16.25                                                   (((setext) =>
% 121.77/16.25                                                     (((emptyI) =>
% 121.77/16.25                                                       (((noeltsimpempty) =>
% 121.77/16.25                                                         (((setbeta) =>
% 121.77/16.25                                                           (((nonemptyE1) =>
% 121.77/16.25                                                             (((nonemptyI) =>
% 121.77/16.25                                                               (((nonemptyI1) =>
% 121.77/16.25                                                                 (((setadjoinIL) =>
% 121.77/16.25                                                                   (((emptyinunitempty) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (setadjoinIR) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (setadjoinE) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (setadjoinOr) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (setoftrueEq) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (powersetI) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (emptyinPowerset) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (emptyInPowerset) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (powersetE) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (setunionI) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (setunionE) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (subPowSU) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (exuE2) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (nonemptyImpWitness) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (uniqinunit) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (notinsingleton) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (eqinunit) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (singletonsswitch) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (upairsetE) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (upairsetIL) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (upairsetIR) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (emptyE1) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (vacuousDall) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (quantDeMorgan1) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (quantDeMorgan2) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (quantDeMorgan3) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (quantDeMorgan4) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (prop2setI) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (prop2set2propI) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (notdexE) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (notdallE) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (exuI1) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (exuI3) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (exuI2) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (inCongP) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (in__Cong) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (exuE3u) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (exu__Cong) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (emptyset__Cong) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (setadjoin__Cong) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (powerset__Cong) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (setunion__Cong) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (omega__Cong) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (exuEu) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (descr__Cong) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (dsetconstr__Cong) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (subsetI1) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (eqimpsubset2) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (eqimpsubset1) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (subsetI2) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (emptysetsubset) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (subsetE) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (subsetE2) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (notsubsetI) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (notequalI1) =>
% 121.77/16.25                                                                     ((
% 121.77/16.25                                                                     (notequalI2) =>
% 121.77/16.25                                                                     ((
% 121.77/16.26                                                                     (subsetRefl) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTrans) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subset2powerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetemptysetimpeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2IR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (disjointsetsI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (bs114d) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusERneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusELneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusILneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusIRneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (secondinupair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairiskpair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsubunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairinpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsuniq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR11) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR12) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairequniteq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempaircEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrERa) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcImageSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (apProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (app) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (infuncsetfunc) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcinfuncset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcextLem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2lamEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrue) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueorfalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTELcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTERcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTnotintersectT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementImpComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contraSubsetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTcontraSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTILcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTIRcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTEcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule0) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1SetBreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (choice2fnsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compEex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionCommutes) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2W) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2A) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2B) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Equiv) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncInj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (leftInvIsSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjCantorThm) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (foundation2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSclos) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peano0notS) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peanoSinj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ordinalMinLem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (!!) @ (
% 121.77/16.26                                                                     ^[Y0 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (ordinal @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y1 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y2 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y2 @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ 
% 121.77/16.26                                                                      Y2) =>
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.26      inference('cnf', [status(esa)], [zf_stmt_0])).
% 121.77/16.26  thf(omega0Ax, axiom,(( omega0Ax  ) = ((in @ emptyset @ omega)))).
% 121.77/16.26  thf('0', plain, (( omega0Ax ) = ( in @ emptyset @ omega )),
% 121.77/16.26      define([status(thm)])).
% 121.77/16.26  thf(emptyinunitempty, axiom,(( emptyinunitempty  ) =
% 121.77/16.26    ((in @ emptyset @ (setadjoin @ emptyset @ emptyset))))).
% 121.77/16.26  thf('1', plain,
% 121.77/16.26      (( emptyinunitempty ) =
% 121.77/16.26       ( in @ emptyset @ ( setadjoin @ emptyset @ emptyset ) )),
% 121.77/16.26      define([status(thm)])).
% 121.77/16.26  thf(emptyset__Cong, axiom,(( emptyset__Cong  ) =
% 121.77/16.26    ((((emptyset) = (emptyset)))))).
% 121.77/16.26  thf('2', plain, (( emptyset__Cong ) = ( ( emptyset ) = ( emptyset ) )),
% 121.77/16.26      define([status(thm)])).
% 121.77/16.26  thf(omega__Cong, axiom,(( omega__Cong  ) = ((((omega) = (omega)))))).
% 121.77/16.26  thf('3', plain, (( omega__Cong ) = ( ( omega ) = ( omega ) )),
% 121.77/16.26      define([status(thm)])).
% 121.77/16.26  thf(zip_derived_cl1, plain,
% 121.77/16.26      (~ (((setextAx) =>
% 121.77/16.26           (((emptysetAx) =>
% 121.77/16.26             (((setadjoinAx) =>
% 121.77/16.26               (((powersetAx) =>
% 121.77/16.26                 (((setunionAx) =>
% 121.77/16.26                   (((in @ emptyset @ omega) =>
% 121.77/16.26                     (((omegaSAx) =>
% 121.77/16.26                       (((omegaIndAx) =>
% 121.77/16.26                         (((replAx) =>
% 121.77/16.26                           (((foundationAx) =>
% 121.77/16.26                             (((wellorderingAx) =>
% 121.77/16.26                               (((descrp) =>
% 121.77/16.26                                 (((dsetconstrI) =>
% 121.77/16.26                                   (((dsetconstrEL) =>
% 121.77/16.26                                     (((dsetconstrER) =>
% 121.77/16.26                                       (((exuE1) =>
% 121.77/16.26                                         (((prop2setE) =>
% 121.77/16.26                                           (((emptysetE) =>
% 121.77/16.26                                             (((emptysetimpfalse) =>
% 121.77/16.26                                               (((notinemptyset) =>
% 121.77/16.26                                                 (((exuE3e) =>
% 121.77/16.26                                                   (((setext) =>
% 121.77/16.26                                                     (((emptyI) =>
% 121.77/16.26                                                       (((noeltsimpempty) =>
% 121.77/16.26                                                         (((setbeta) =>
% 121.77/16.26                                                           (((nonemptyE1) =>
% 121.77/16.26                                                             (((nonemptyI) =>
% 121.77/16.26                                                               (((nonemptyI1) =>
% 121.77/16.26                                                                 (((setadjoinIL) =>
% 121.77/16.26                                                                   (((in @ 
% 121.77/16.26                                                                     emptyset @ 
% 121.77/16.26                                                                     (setadjoin @ 
% 121.77/16.26                                                                      emptyset @ 
% 121.77/16.26                                                                      emptyset)) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinOr) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setoftrueEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyinPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subPowSU) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (nonemptyImpWitness) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (uniqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsswitch) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (vacuousDall) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2setI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2set2propI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdexE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdallE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inCongP) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (in__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE3u) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exu__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyset) =
% 121.77/16.26                                                                     (emptyset))) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoin__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powerset__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunion__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omega) =
% 121.77/16.26                                                                     (omega))) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuEu) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (descr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dsetconstr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptysetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notsubsetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetRefl) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTrans) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subset2powerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetemptysetimpeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2IR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (disjointsetsI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (bs114d) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusERneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusELneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusILneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusIRneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (secondinupair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairiskpair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsubunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairinpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsuniq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR11) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR12) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairequniteq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempaircEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrERa) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcImageSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (apProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (app) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (infuncsetfunc) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcinfuncset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcextLem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2lamEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrue) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueorfalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTELcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTERcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTnotintersectT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementImpComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contraSubsetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTcontraSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTILcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTIRcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTEcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule0) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1SetBreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (choice2fnsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compEex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionCommutes) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2W) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2A) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2B) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Equiv) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncInj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (leftInvIsSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjCantorThm) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (foundation2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSclos) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peano0notS) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peanoSinj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ordinalMinLem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (!!) @ (
% 121.77/16.26                                                                     ^[Y0 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (ordinal @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y1 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y2 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y2 @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ 
% 121.77/16.26                                                                      Y2) =>
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.26      inference('rw', [status(thm)], [zip_derived_cl0, '0', '1', '2', '3'])).
% 121.77/16.26  thf(zip_derived_cl2, plain,
% 121.77/16.26      (~ (((setextAx) =>
% 121.77/16.26           (((emptysetAx) =>
% 121.77/16.26             (((setadjoinAx) =>
% 121.77/16.26               (((powersetAx) =>
% 121.77/16.26                 (((setunionAx) =>
% 121.77/16.26                   (((in @ emptyset @ omega) =>
% 121.77/16.26                     (((omegaSAx) =>
% 121.77/16.26                       (((omegaIndAx) =>
% 121.77/16.26                         (((replAx) =>
% 121.77/16.26                           (((foundationAx) =>
% 121.77/16.26                             (((wellorderingAx) =>
% 121.77/16.26                               (((descrp) =>
% 121.77/16.26                                 (((dsetconstrI) =>
% 121.77/16.26                                   (((dsetconstrEL) =>
% 121.77/16.26                                     (((dsetconstrER) =>
% 121.77/16.26                                       (((exuE1) =>
% 121.77/16.26                                         (((prop2setE) =>
% 121.77/16.26                                           (((emptysetE) =>
% 121.77/16.26                                             (((emptysetimpfalse) =>
% 121.77/16.26                                               (((notinemptyset) =>
% 121.77/16.26                                                 (((exuE3e) =>
% 121.77/16.26                                                   (((setext) =>
% 121.77/16.26                                                     (((emptyI) =>
% 121.77/16.26                                                       (((noeltsimpempty) =>
% 121.77/16.26                                                         (((setbeta) =>
% 121.77/16.26                                                           (((nonemptyE1) =>
% 121.77/16.26                                                             (((nonemptyI) =>
% 121.77/16.26                                                               (((nonemptyI1) =>
% 121.77/16.26                                                                 (((setadjoinIL) =>
% 121.77/16.26                                                                   (((in @ 
% 121.77/16.26                                                                     emptyset @ 
% 121.77/16.26                                                                     (setadjoin @ 
% 121.77/16.26                                                                      emptyset @ 
% 121.77/16.26                                                                      emptyset)) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinOr) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setoftrueEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyinPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subPowSU) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (nonemptyImpWitness) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (uniqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsswitch) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (vacuousDall) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2setI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2set2propI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdexE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdallE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inCongP) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (in__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE3u) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exu__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoin__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powerset__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunion__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuEu) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (descr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dsetconstr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptysetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notsubsetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetRefl) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTrans) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subset2powerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetemptysetimpeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2IR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (disjointsetsI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (bs114d) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusERneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusELneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusILneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusIRneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (secondinupair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairiskpair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsubunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairinpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsuniq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR11) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR12) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairequniteq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempaircEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrERa) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcImageSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (apProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (app) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (infuncsetfunc) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcinfuncset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcextLem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2lamEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrue) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueorfalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTELcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTERcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTnotintersectT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementImpComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contraSubsetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTcontraSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTILcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTIRcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTEcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule0) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1SetBreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (choice2fnsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compEex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionCommutes) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2W) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2A) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2B) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Equiv) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncInj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (leftInvIsSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjCantorThm) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (foundation2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSclos) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peano0notS) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peanoSinj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ordinalMinLem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (!!) @ (
% 121.77/16.26                                                                     ^[Y0 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (ordinal @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y1 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y2 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y2 @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ 
% 121.77/16.26                                                                      Y2) =>
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.26      inference('simplify boolean subterms', [status(thm)], [zip_derived_cl1])).
% 121.77/16.26  thf(zip_derived_cl4, plain,
% 121.77/16.26      (~ (((emptysetAx) =>
% 121.77/16.26           (((setadjoinAx) =>
% 121.77/16.26             (((powersetAx) =>
% 121.77/16.26               (((setunionAx) =>
% 121.77/16.26                 (((in @ emptyset @ omega) =>
% 121.77/16.26                   (((omegaSAx) =>
% 121.77/16.26                     (((omegaIndAx) =>
% 121.77/16.26                       (((replAx) =>
% 121.77/16.26                         (((foundationAx) =>
% 121.77/16.26                           (((wellorderingAx) =>
% 121.77/16.26                             (((descrp) =>
% 121.77/16.26                               (((dsetconstrI) =>
% 121.77/16.26                                 (((dsetconstrEL) =>
% 121.77/16.26                                   (((dsetconstrER) =>
% 121.77/16.26                                     (((exuE1) =>
% 121.77/16.26                                       (((prop2setE) =>
% 121.77/16.26                                         (((emptysetE) =>
% 121.77/16.26                                           (((emptysetimpfalse) =>
% 121.77/16.26                                             (((notinemptyset) =>
% 121.77/16.26                                               (((exuE3e) =>
% 121.77/16.26                                                 (((setext) =>
% 121.77/16.26                                                   (((emptyI) =>
% 121.77/16.26                                                     (((noeltsimpempty) =>
% 121.77/16.26                                                       (((setbeta) =>
% 121.77/16.26                                                         (((nonemptyE1) =>
% 121.77/16.26                                                           (((nonemptyI) =>
% 121.77/16.26                                                             (((nonemptyI1) =>
% 121.77/16.26                                                               (((setadjoinIL) =>
% 121.77/16.26                                                                 (((in @ 
% 121.77/16.26                                                                   emptyset @ 
% 121.77/16.26                                                                   (setadjoin @ 
% 121.77/16.26                                                                    emptyset @ 
% 121.77/16.26                                                                    emptyset)) =>
% 121.77/16.26                                                                   (((setadjoinIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinOr) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setoftrueEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyinPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subPowSU) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (nonemptyImpWitness) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (uniqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsswitch) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (vacuousDall) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2setI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2set2propI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdexE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdallE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inCongP) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (in__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE3u) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exu__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoin__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powerset__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunion__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuEu) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (descr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dsetconstr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptysetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notsubsetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetRefl) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTrans) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subset2powerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetemptysetimpeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2IR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (disjointsetsI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (bs114d) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusERneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusELneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusILneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusIRneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (secondinupair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairiskpair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsubunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairinpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsuniq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR11) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR12) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairequniteq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempaircEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrERa) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcImageSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (apProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (app) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (infuncsetfunc) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcinfuncset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcextLem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2lamEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrue) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueorfalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTELcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTERcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTnotintersectT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementImpComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contraSubsetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTcontraSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTILcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTIRcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTEcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule0) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1SetBreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (choice2fnsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compEex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionCommutes) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2W) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2A) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2B) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Equiv) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncInj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (leftInvIsSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjCantorThm) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (foundation2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSclos) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peano0notS) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peanoSinj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ordinalMinLem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (!!) @ (
% 121.77/16.26                                                                     ^[Y0 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (ordinal @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y1 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y2 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y2 @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ 
% 121.77/16.26                                                                      Y2) =>
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.26      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2])).
% 121.77/16.26  thf(zip_derived_cl7, plain,
% 121.77/16.26      (~ (((setadjoinAx) =>
% 121.77/16.26           (((powersetAx) =>
% 121.77/16.26             (((setunionAx) =>
% 121.77/16.26               (((in @ emptyset @ omega) =>
% 121.77/16.26                 (((omegaSAx) =>
% 121.77/16.26                   (((omegaIndAx) =>
% 121.77/16.26                     (((replAx) =>
% 121.77/16.26                       (((foundationAx) =>
% 121.77/16.26                         (((wellorderingAx) =>
% 121.77/16.26                           (((descrp) =>
% 121.77/16.26                             (((dsetconstrI) =>
% 121.77/16.26                               (((dsetconstrEL) =>
% 121.77/16.26                                 (((dsetconstrER) =>
% 121.77/16.26                                   (((exuE1) =>
% 121.77/16.26                                     (((prop2setE) =>
% 121.77/16.26                                       (((emptysetE) =>
% 121.77/16.26                                         (((emptysetimpfalse) =>
% 121.77/16.26                                           (((notinemptyset) =>
% 121.77/16.26                                             (((exuE3e) =>
% 121.77/16.26                                               (((setext) =>
% 121.77/16.26                                                 (((emptyI) =>
% 121.77/16.26                                                   (((noeltsimpempty) =>
% 121.77/16.26                                                     (((setbeta) =>
% 121.77/16.26                                                       (((nonemptyE1) =>
% 121.77/16.26                                                         (((nonemptyI) =>
% 121.77/16.26                                                           (((nonemptyI1) =>
% 121.77/16.26                                                             (((setadjoinIL) =>
% 121.77/16.26                                                               (((in @ 
% 121.77/16.26                                                                 emptyset @ 
% 121.77/16.26                                                                 (setadjoin @ 
% 121.77/16.26                                                                  emptyset @ 
% 121.77/16.26                                                                  emptyset)) =>
% 121.77/16.26                                                                 (((setadjoinIR) =>
% 121.77/16.26                                                                   (((setadjoinE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinOr) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setoftrueEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyinPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subPowSU) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (nonemptyImpWitness) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (uniqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsswitch) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (vacuousDall) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2setI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2set2propI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdexE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdallE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inCongP) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (in__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE3u) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exu__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoin__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powerset__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunion__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuEu) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (descr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dsetconstr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptysetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notsubsetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetRefl) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTrans) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subset2powerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetemptysetimpeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2IR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (disjointsetsI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (bs114d) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusERneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusELneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusILneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusIRneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (secondinupair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairiskpair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsubunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairinpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsuniq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR11) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR12) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairequniteq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempaircEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrERa) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcImageSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (apProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (app) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (infuncsetfunc) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcinfuncset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcextLem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2lamEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrue) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueorfalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTELcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTERcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTnotintersectT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementImpComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contraSubsetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTcontraSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTILcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTIRcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTEcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule0) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1SetBreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (choice2fnsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compEex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionCommutes) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2W) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2A) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2B) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Equiv) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncInj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (leftInvIsSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjCantorThm) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (foundation2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSclos) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peano0notS) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peanoSinj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ordinalMinLem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (!!) @ (
% 121.77/16.26                                                                     ^[Y0 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (ordinal @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y1 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y2 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y2 @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ 
% 121.77/16.26                                                                      Y2) =>
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.26      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl4])).
% 121.77/16.26  thf(zip_derived_cl11, plain,
% 121.77/16.26      (~ (((powersetAx) =>
% 121.77/16.26           (((setunionAx) =>
% 121.77/16.26             (((in @ emptyset @ omega) =>
% 121.77/16.26               (((omegaSAx) =>
% 121.77/16.26                 (((omegaIndAx) =>
% 121.77/16.26                   (((replAx) =>
% 121.77/16.26                     (((foundationAx) =>
% 121.77/16.26                       (((wellorderingAx) =>
% 121.77/16.26                         (((descrp) =>
% 121.77/16.26                           (((dsetconstrI) =>
% 121.77/16.26                             (((dsetconstrEL) =>
% 121.77/16.26                               (((dsetconstrER) =>
% 121.77/16.26                                 (((exuE1) =>
% 121.77/16.26                                   (((prop2setE) =>
% 121.77/16.26                                     (((emptysetE) =>
% 121.77/16.26                                       (((emptysetimpfalse) =>
% 121.77/16.26                                         (((notinemptyset) =>
% 121.77/16.26                                           (((exuE3e) =>
% 121.77/16.26                                             (((setext) =>
% 121.77/16.26                                               (((emptyI) =>
% 121.77/16.26                                                 (((noeltsimpempty) =>
% 121.77/16.26                                                   (((setbeta) =>
% 121.77/16.26                                                     (((nonemptyE1) =>
% 121.77/16.26                                                       (((nonemptyI) =>
% 121.77/16.26                                                         (((nonemptyI1) =>
% 121.77/16.26                                                           (((setadjoinIL) =>
% 121.77/16.26                                                             (((in @ 
% 121.77/16.26                                                               emptyset @ 
% 121.77/16.26                                                               (setadjoin @ 
% 121.77/16.26                                                                emptyset @ 
% 121.77/16.26                                                                emptyset)) =>
% 121.77/16.26                                                               (((setadjoinIR) =>
% 121.77/16.26                                                                 (((setadjoinE) =>
% 121.77/16.26                                                                   (((setadjoinOr) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setoftrueEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyinPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subPowSU) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (nonemptyImpWitness) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (uniqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsswitch) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (vacuousDall) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2setI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2set2propI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdexE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdallE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inCongP) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (in__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE3u) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exu__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoin__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powerset__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunion__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuEu) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (descr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dsetconstr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptysetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notsubsetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetRefl) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTrans) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subset2powerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetemptysetimpeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2IR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (disjointsetsI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (bs114d) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusERneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusELneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusILneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusIRneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (secondinupair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairiskpair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsubunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairinpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsuniq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR11) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR12) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairequniteq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempaircEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrERa) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcImageSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (apProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (app) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (infuncsetfunc) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcinfuncset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcextLem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2lamEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrue) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueorfalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTELcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTERcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTnotintersectT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementImpComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contraSubsetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTcontraSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTILcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTIRcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTEcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule0) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1SetBreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (choice2fnsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compEex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionCommutes) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2W) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2A) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2B) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Equiv) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncInj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (leftInvIsSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjCantorThm) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (foundation2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSclos) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peano0notS) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peanoSinj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ordinalMinLem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (!!) @ (
% 121.77/16.26                                                                     ^[Y0 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (ordinal @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y1 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y2 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y2 @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ 
% 121.77/16.26                                                                      Y2) =>
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.26      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl7])).
% 121.77/16.26  thf(zip_derived_cl16, plain,
% 121.77/16.26      (~ (((setunionAx) =>
% 121.77/16.26           (((in @ emptyset @ omega) =>
% 121.77/16.26             (((omegaSAx) =>
% 121.77/16.26               (((omegaIndAx) =>
% 121.77/16.26                 (((replAx) =>
% 121.77/16.26                   (((foundationAx) =>
% 121.77/16.26                     (((wellorderingAx) =>
% 121.77/16.26                       (((descrp) =>
% 121.77/16.26                         (((dsetconstrI) =>
% 121.77/16.26                           (((dsetconstrEL) =>
% 121.77/16.26                             (((dsetconstrER) =>
% 121.77/16.26                               (((exuE1) =>
% 121.77/16.26                                 (((prop2setE) =>
% 121.77/16.26                                   (((emptysetE) =>
% 121.77/16.26                                     (((emptysetimpfalse) =>
% 121.77/16.26                                       (((notinemptyset) =>
% 121.77/16.26                                         (((exuE3e) =>
% 121.77/16.26                                           (((setext) =>
% 121.77/16.26                                             (((emptyI) =>
% 121.77/16.26                                               (((noeltsimpempty) =>
% 121.77/16.26                                                 (((setbeta) =>
% 121.77/16.26                                                   (((nonemptyE1) =>
% 121.77/16.26                                                     (((nonemptyI) =>
% 121.77/16.26                                                       (((nonemptyI1) =>
% 121.77/16.26                                                         (((setadjoinIL) =>
% 121.77/16.26                                                           (((in @ emptyset @ 
% 121.77/16.26                                                             (setadjoin @ 
% 121.77/16.26                                                              emptyset @ 
% 121.77/16.26                                                              emptyset)) =>
% 121.77/16.26                                                             (((setadjoinIR) =>
% 121.77/16.26                                                               (((setadjoinE) =>
% 121.77/16.26                                                                 (((setadjoinOr) =>
% 121.77/16.26                                                                   (((setoftrueEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyinPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subPowSU) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (nonemptyImpWitness) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (uniqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsswitch) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (vacuousDall) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2setI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2set2propI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdexE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdallE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inCongP) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (in__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE3u) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exu__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoin__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powerset__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunion__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuEu) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (descr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dsetconstr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptysetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notsubsetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetRefl) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTrans) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subset2powerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetemptysetimpeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2IR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (disjointsetsI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (bs114d) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusERneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusELneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusILneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusIRneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (secondinupair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairiskpair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsubunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairinpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsuniq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR11) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR12) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairequniteq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempaircEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrERa) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcImageSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (apProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (app) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (infuncsetfunc) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcinfuncset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcextLem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2lamEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrue) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueorfalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTELcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTERcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTnotintersectT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementImpComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contraSubsetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTcontraSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTILcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTIRcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTEcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule0) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1SetBreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (choice2fnsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compEex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionCommutes) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2W) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2A) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2B) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Equiv) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncInj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (leftInvIsSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjCantorThm) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (foundation2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSclos) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peano0notS) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peanoSinj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ordinalMinLem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (!!) @ (
% 121.77/16.26                                                                     ^[Y0 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (ordinal @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y1 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y2 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y2 @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ 
% 121.77/16.26                                                                      Y2) =>
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.26      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])).
% 121.77/16.26  thf(zip_derived_cl21, plain,
% 121.77/16.26      (~ (((in @ emptyset @ omega) =>
% 121.77/16.26           (((omegaSAx) =>
% 121.77/16.26             (((omegaIndAx) =>
% 121.77/16.26               (((replAx) =>
% 121.77/16.26                 (((foundationAx) =>
% 121.77/16.26                   (((wellorderingAx) =>
% 121.77/16.26                     (((descrp) =>
% 121.77/16.26                       (((dsetconstrI) =>
% 121.77/16.26                         (((dsetconstrEL) =>
% 121.77/16.26                           (((dsetconstrER) =>
% 121.77/16.26                             (((exuE1) =>
% 121.77/16.26                               (((prop2setE) =>
% 121.77/16.26                                 (((emptysetE) =>
% 121.77/16.26                                   (((emptysetimpfalse) =>
% 121.77/16.26                                     (((notinemptyset) =>
% 121.77/16.26                                       (((exuE3e) =>
% 121.77/16.26                                         (((setext) =>
% 121.77/16.26                                           (((emptyI) =>
% 121.77/16.26                                             (((noeltsimpempty) =>
% 121.77/16.26                                               (((setbeta) =>
% 121.77/16.26                                                 (((nonemptyE1) =>
% 121.77/16.26                                                   (((nonemptyI) =>
% 121.77/16.26                                                     (((nonemptyI1) =>
% 121.77/16.26                                                       (((setadjoinIL) =>
% 121.77/16.26                                                         (((in @ emptyset @ 
% 121.77/16.26                                                           (setadjoin @ 
% 121.77/16.26                                                            emptyset @ emptyset)) =>
% 121.77/16.26                                                           (((setadjoinIR) =>
% 121.77/16.26                                                             (((setadjoinE) =>
% 121.77/16.26                                                               (((setadjoinOr) =>
% 121.77/16.26                                                                 (((setoftrueEq) =>
% 121.77/16.26                                                                   (((powersetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyinPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subPowSU) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (nonemptyImpWitness) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (uniqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsswitch) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (vacuousDall) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2setI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2set2propI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdexE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdallE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inCongP) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (in__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE3u) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exu__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoin__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powerset__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunion__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuEu) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (descr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dsetconstr__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqimpsubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptysetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notsubsetI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notequalI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetRefl) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTrans) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setadjoinSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subset2powerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetemptysetimpeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (sepSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2IR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (disjointsetsI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectRsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (bs114d) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusERneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusELneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusILneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusIRneg) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusLsub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusSubset1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (symdiffIneg2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (secondinupair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairiskpair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletoninpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairset2E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsubunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairinpowunion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ubforcartprodlem3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempair) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1I2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsuniq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR11) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR12) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairequniteq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setukpairinjR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ksndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (kpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndin) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemEL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairmemER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodmempaircEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodfstpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodsndpairEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (cartprodpairsurjEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrSub) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrERa) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrEL2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (dpsetconstrER) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcImageSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (apProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (app) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (infuncsetfunc) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcinfuncset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamProp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lamp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2p) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (brelnall2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ex1E2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcextLem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcGraphProp4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (funcext2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ap2apEq2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (lam2lamEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (beta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eta2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalseProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueProp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifSingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ifp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (theeq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrue) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iffalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (iftrueorfalse) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setminusT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementT_lem) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setextT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subsetTI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTELcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintersectTERcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contrasubsetT3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementSub2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (doubleComplementEq) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTnotintersectT) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementImpComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (contraSubsetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementTcontraSubset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTILcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTIRcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binunionTEcontra) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2a) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2b) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (demorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule0) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz13rule4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz1_5) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1SetBreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (choice2fnsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1all1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqbreln1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1invE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1compEex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionprop) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionEcases) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (breln1unionCommutes) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2W) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2A) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (woz2B) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Ex1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1Equiv) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1E) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (image1I) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (injFuncSetFuncInj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (leftInvIsSurj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (surjCantorThm) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (foundation2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinself2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSp) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (omegaSclos) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peano0notS) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (peanoSinj) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (binintTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (transitivesetOp2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionTransitive) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (ordinalMinLem1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (!!) @ (
% 121.77/16.26                                                                     ^[Y0 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (ordinal @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y1 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (!!) @ (
% 121.77/16.26                                                                      ^[Y2 : $i]:
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y2 @ 
% 121.77/16.26                                                                      Y0) =>
% 121.77/16.26                                                                      ((
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ 
% 121.77/16.26                                                                      Y2) =>
% 121.77/16.26                                                                      (in @ 
% 121.77/16.26                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.26      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl16])).
% 121.77/16.26  thf(zip_derived_cl28, plain,
% 121.77/16.26      (~ (((omegaSAx) =>
% 121.77/16.26           (((omegaIndAx) =>
% 121.77/16.26             (((replAx) =>
% 121.77/16.26               (((foundationAx) =>
% 121.77/16.26                 (((wellorderingAx) =>
% 121.77/16.26                   (((descrp) =>
% 121.77/16.26                     (((dsetconstrI) =>
% 121.77/16.26                       (((dsetconstrEL) =>
% 121.77/16.26                         (((dsetconstrER) =>
% 121.77/16.26                           (((exuE1) =>
% 121.77/16.26                             (((prop2setE) =>
% 121.77/16.26                               (((emptysetE) =>
% 121.77/16.26                                 (((emptysetimpfalse) =>
% 121.77/16.26                                   (((notinemptyset) =>
% 121.77/16.26                                     (((exuE3e) =>
% 121.77/16.26                                       (((setext) =>
% 121.77/16.26                                         (((emptyI) =>
% 121.77/16.26                                           (((noeltsimpempty) =>
% 121.77/16.26                                             (((setbeta) =>
% 121.77/16.26                                               (((nonemptyE1) =>
% 121.77/16.26                                                 (((nonemptyI) =>
% 121.77/16.26                                                   (((nonemptyI1) =>
% 121.77/16.26                                                     (((setadjoinIL) =>
% 121.77/16.26                                                       (((in @ emptyset @ 
% 121.77/16.26                                                         (setadjoin @ 
% 121.77/16.26                                                          emptyset @ emptyset)) =>
% 121.77/16.26                                                         (((setadjoinIR) =>
% 121.77/16.26                                                           (((setadjoinE) =>
% 121.77/16.26                                                             (((setadjoinOr) =>
% 121.77/16.26                                                               (((setoftrueEq) =>
% 121.77/16.26                                                                 (((powersetI) =>
% 121.77/16.26                                                                   (((emptyinPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyInPowerset) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (powersetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (setunionE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (subPowSU) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (nonemptyImpWitness) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (uniqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notinsingleton) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (eqinunit) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (singletonsswitch) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIL) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (upairsetIR) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (emptyE1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (vacuousDall) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (quantDeMorgan4) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2setI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (prop2set2propI) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdexE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (notdallE) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI1) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI3) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuI2) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (inCongP) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (in__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exuE3u) =>
% 121.77/16.26                                                                     ((
% 121.77/16.26                                                                     (exu__Cong) =>
% 121.77/16.26                                                                     ((
% 121.77/16.27                                                                     (setadjoin__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powerset__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunion__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuEu) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (descr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dsetconstr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptysetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notsubsetI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetRefl) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTrans) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subset2powerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetemptysetimpeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepInPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2IR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (disjointsetsI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (bs114d) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusERneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusELneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusILneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusIRneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (secondinupair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairiskpair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsubunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairinpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsuniq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR11) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR12) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairequniteq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempaircEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrERa) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcImageSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (apProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (app) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (infuncsetfunc) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcinfuncset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcextLem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2lamEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrue) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueorfalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTELcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTERcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTnotintersectT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementImpComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contraSubsetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTcontraSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTILcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTIRcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTEcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule0) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1SetBreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (choice2fnsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compEex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionCommutes) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2W) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2A) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2B) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Equiv) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncInj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (leftInvIsSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjCantorThm) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (foundation2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSclos) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peano0notS) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peanoSinj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ordinalMinLem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (!!) @ (
% 121.77/16.27                                                                     ^[Y0 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (ordinal @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y1 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y2 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y2 @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ 
% 121.77/16.27                                                                      Y2) =>
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.27      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl21])).
% 121.77/16.27  thf(zip_derived_cl34, plain,
% 121.77/16.27      (~ (((omegaIndAx) =>
% 121.77/16.27           (((replAx) =>
% 121.77/16.27             (((foundationAx) =>
% 121.77/16.27               (((wellorderingAx) =>
% 121.77/16.27                 (((descrp) =>
% 121.77/16.27                   (((dsetconstrI) =>
% 121.77/16.27                     (((dsetconstrEL) =>
% 121.77/16.27                       (((dsetconstrER) =>
% 121.77/16.27                         (((exuE1) =>
% 121.77/16.27                           (((prop2setE) =>
% 121.77/16.27                             (((emptysetE) =>
% 121.77/16.27                               (((emptysetimpfalse) =>
% 121.77/16.27                                 (((notinemptyset) =>
% 121.77/16.27                                   (((exuE3e) =>
% 121.77/16.27                                     (((setext) =>
% 121.77/16.27                                       (((emptyI) =>
% 121.77/16.27                                         (((noeltsimpempty) =>
% 121.77/16.27                                           (((setbeta) =>
% 121.77/16.27                                             (((nonemptyE1) =>
% 121.77/16.27                                               (((nonemptyI) =>
% 121.77/16.27                                                 (((nonemptyI1) =>
% 121.77/16.27                                                   (((setadjoinIL) =>
% 121.77/16.27                                                     (((in @ emptyset @ 
% 121.77/16.27                                                       (setadjoin @ emptyset @ 
% 121.77/16.27                                                        emptyset)) =>
% 121.77/16.27                                                       (((setadjoinIR) =>
% 121.77/16.27                                                         (((setadjoinE) =>
% 121.77/16.27                                                           (((setadjoinOr) =>
% 121.77/16.27                                                             (((setoftrueEq) =>
% 121.77/16.27                                                               (((powersetI) =>
% 121.77/16.27                                                                 (((emptyinPowerset) =>
% 121.77/16.27                                                                   (((emptyInPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subPowSU) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (nonemptyImpWitness) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (uniqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsswitch) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptyE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (vacuousDall) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2setI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2set2propI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdexE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdallE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inCongP) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (in__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE3u) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exu__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoin__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powerset__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunion__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuEu) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (descr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dsetconstr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptysetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notsubsetI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetRefl) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTrans) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subset2powerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetemptysetimpeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepInPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2IR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (disjointsetsI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (bs114d) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusERneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusELneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusILneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusIRneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (secondinupair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairiskpair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsubunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairinpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsuniq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR11) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR12) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairequniteq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempaircEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrERa) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcImageSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (apProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (app) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (infuncsetfunc) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcinfuncset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcextLem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2lamEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrue) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueorfalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTELcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTERcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTnotintersectT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementImpComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contraSubsetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTcontraSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTILcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTIRcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTEcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule0) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1SetBreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (choice2fnsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compEex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionCommutes) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2W) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2A) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2B) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Equiv) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncInj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (leftInvIsSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjCantorThm) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (foundation2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSclos) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peano0notS) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peanoSinj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ordinalMinLem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (!!) @ (
% 121.77/16.27                                                                     ^[Y0 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (ordinal @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y1 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y2 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y2 @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ 
% 121.77/16.27                                                                      Y2) =>
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.27      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl28])).
% 121.77/16.27  thf(zip_derived_cl40, plain,
% 121.77/16.27      (~ (((replAx) =>
% 121.77/16.27           (((foundationAx) =>
% 121.77/16.27             (((wellorderingAx) =>
% 121.77/16.27               (((descrp) =>
% 121.77/16.27                 (((dsetconstrI) =>
% 121.77/16.27                   (((dsetconstrEL) =>
% 121.77/16.27                     (((dsetconstrER) =>
% 121.77/16.27                       (((exuE1) =>
% 121.77/16.27                         (((prop2setE) =>
% 121.77/16.27                           (((emptysetE) =>
% 121.77/16.27                             (((emptysetimpfalse) =>
% 121.77/16.27                               (((notinemptyset) =>
% 121.77/16.27                                 (((exuE3e) =>
% 121.77/16.27                                   (((setext) =>
% 121.77/16.27                                     (((emptyI) =>
% 121.77/16.27                                       (((noeltsimpempty) =>
% 121.77/16.27                                         (((setbeta) =>
% 121.77/16.27                                           (((nonemptyE1) =>
% 121.77/16.27                                             (((nonemptyI) =>
% 121.77/16.27                                               (((nonemptyI1) =>
% 121.77/16.27                                                 (((setadjoinIL) =>
% 121.77/16.27                                                   (((in @ emptyset @ 
% 121.77/16.27                                                     (setadjoin @ emptyset @ 
% 121.77/16.27                                                      emptyset)) =>
% 121.77/16.27                                                     (((setadjoinIR) =>
% 121.77/16.27                                                       (((setadjoinE) =>
% 121.77/16.27                                                         (((setadjoinOr) =>
% 121.77/16.27                                                           (((setoftrueEq) =>
% 121.77/16.27                                                             (((powersetI) =>
% 121.77/16.27                                                               (((emptyinPowerset) =>
% 121.77/16.27                                                                 (((emptyInPowerset) =>
% 121.77/16.27                                                                   (((powersetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subPowSU) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (nonemptyImpWitness) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (uniqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsswitch) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptyE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (vacuousDall) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2setI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2set2propI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdexE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdallE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inCongP) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (in__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE3u) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exu__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoin__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powerset__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunion__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuEu) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (descr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dsetconstr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptysetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notsubsetI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetRefl) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTrans) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subset2powerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetemptysetimpeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepInPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2IR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (disjointsetsI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (bs114d) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusERneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusELneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusILneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusIRneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (secondinupair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairiskpair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsubunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairinpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsuniq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR11) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR12) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairequniteq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempaircEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrERa) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcImageSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (apProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (app) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (infuncsetfunc) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcinfuncset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcextLem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2lamEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrue) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueorfalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTELcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTERcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTnotintersectT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementImpComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contraSubsetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTcontraSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTILcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTIRcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTEcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule0) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1SetBreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (choice2fnsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compEex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionCommutes) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2W) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2A) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2B) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Equiv) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncInj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (leftInvIsSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjCantorThm) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (foundation2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSclos) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peano0notS) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peanoSinj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ordinalMinLem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (!!) @ (
% 121.77/16.27                                                                     ^[Y0 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (ordinal @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y1 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y2 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y2 @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ 
% 121.77/16.27                                                                      Y2) =>
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.27      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl34])).
% 121.77/16.27  thf(zip_derived_cl45, plain,
% 121.77/16.27      (~ (((foundationAx) =>
% 121.77/16.27           (((wellorderingAx) =>
% 121.77/16.27             (((descrp) =>
% 121.77/16.27               (((dsetconstrI) =>
% 121.77/16.27                 (((dsetconstrEL) =>
% 121.77/16.27                   (((dsetconstrER) =>
% 121.77/16.27                     (((exuE1) =>
% 121.77/16.27                       (((prop2setE) =>
% 121.77/16.27                         (((emptysetE) =>
% 121.77/16.27                           (((emptysetimpfalse) =>
% 121.77/16.27                             (((notinemptyset) =>
% 121.77/16.27                               (((exuE3e) =>
% 121.77/16.27                                 (((setext) =>
% 121.77/16.27                                   (((emptyI) =>
% 121.77/16.27                                     (((noeltsimpempty) =>
% 121.77/16.27                                       (((setbeta) =>
% 121.77/16.27                                         (((nonemptyE1) =>
% 121.77/16.27                                           (((nonemptyI) =>
% 121.77/16.27                                             (((nonemptyI1) =>
% 121.77/16.27                                               (((setadjoinIL) =>
% 121.77/16.27                                                 (((in @ emptyset @ 
% 121.77/16.27                                                   (setadjoin @ emptyset @ 
% 121.77/16.27                                                    emptyset)) =>
% 121.77/16.27                                                   (((setadjoinIR) =>
% 121.77/16.27                                                     (((setadjoinE) =>
% 121.77/16.27                                                       (((setadjoinOr) =>
% 121.77/16.27                                                         (((setoftrueEq) =>
% 121.77/16.27                                                           (((powersetI) =>
% 121.77/16.27                                                             (((emptyinPowerset) =>
% 121.77/16.27                                                               (((emptyInPowerset) =>
% 121.77/16.27                                                                 (((powersetE) =>
% 121.77/16.27                                                                   (((setunionI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subPowSU) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (nonemptyImpWitness) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (uniqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsswitch) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptyE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (vacuousDall) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2setI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2set2propI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdexE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdallE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inCongP) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (in__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE3u) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exu__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoin__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powerset__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunion__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuEu) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (descr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dsetconstr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptysetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notsubsetI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetRefl) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTrans) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subset2powerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetemptysetimpeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepInPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2IR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (disjointsetsI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (bs114d) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusERneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusELneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusILneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusIRneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (secondinupair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairiskpair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsubunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairinpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsuniq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR11) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR12) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairequniteq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempaircEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrERa) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcImageSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (apProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (app) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (infuncsetfunc) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcinfuncset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcextLem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2lamEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrue) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueorfalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTELcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTERcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTnotintersectT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementImpComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contraSubsetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTcontraSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTILcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTIRcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTEcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule0) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1SetBreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (choice2fnsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compEex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionCommutes) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2W) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2A) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2B) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Equiv) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncInj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (leftInvIsSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjCantorThm) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (foundation2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSclos) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peano0notS) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peanoSinj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ordinalMinLem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (!!) @ (
% 121.77/16.27                                                                     ^[Y0 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (ordinal @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y1 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y2 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y2 @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ 
% 121.77/16.27                                                                      Y2) =>
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.27      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl40])).
% 121.77/16.27  thf(zip_derived_cl50, plain,
% 121.77/16.27      (~ (((wellorderingAx) =>
% 121.77/16.27           (((descrp) =>
% 121.77/16.27             (((dsetconstrI) =>
% 121.77/16.27               (((dsetconstrEL) =>
% 121.77/16.27                 (((dsetconstrER) =>
% 121.77/16.27                   (((exuE1) =>
% 121.77/16.27                     (((prop2setE) =>
% 121.77/16.27                       (((emptysetE) =>
% 121.77/16.27                         (((emptysetimpfalse) =>
% 121.77/16.27                           (((notinemptyset) =>
% 121.77/16.27                             (((exuE3e) =>
% 121.77/16.27                               (((setext) =>
% 121.77/16.27                                 (((emptyI) =>
% 121.77/16.27                                   (((noeltsimpempty) =>
% 121.77/16.27                                     (((setbeta) =>
% 121.77/16.27                                       (((nonemptyE1) =>
% 121.77/16.27                                         (((nonemptyI) =>
% 121.77/16.27                                           (((nonemptyI1) =>
% 121.77/16.27                                             (((setadjoinIL) =>
% 121.77/16.27                                               (((in @ emptyset @ 
% 121.77/16.27                                                 (setadjoin @ emptyset @ 
% 121.77/16.27                                                  emptyset)) =>
% 121.77/16.27                                                 (((setadjoinIR) =>
% 121.77/16.27                                                   (((setadjoinE) =>
% 121.77/16.27                                                     (((setadjoinOr) =>
% 121.77/16.27                                                       (((setoftrueEq) =>
% 121.77/16.27                                                         (((powersetI) =>
% 121.77/16.27                                                           (((emptyinPowerset) =>
% 121.77/16.27                                                             (((emptyInPowerset) =>
% 121.77/16.27                                                               (((powersetE) =>
% 121.77/16.27                                                                 (((setunionI) =>
% 121.77/16.27                                                                   (((setunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subPowSU) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (nonemptyImpWitness) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (uniqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsswitch) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptyE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (vacuousDall) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2setI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2set2propI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdexE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdallE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inCongP) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (in__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE3u) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exu__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoin__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powerset__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunion__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuEu) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (descr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dsetconstr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptysetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notsubsetI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetRefl) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTrans) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subset2powerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetemptysetimpeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepInPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2IR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (disjointsetsI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (bs114d) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusERneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusELneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusILneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusIRneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (secondinupair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairiskpair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsubunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairinpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsuniq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR11) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR12) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairequniteq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempaircEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrERa) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcImageSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (apProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (app) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (infuncsetfunc) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcinfuncset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcextLem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2lamEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrue) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueorfalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTELcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTERcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTnotintersectT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementImpComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contraSubsetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTcontraSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTILcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTIRcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTEcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule0) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1SetBreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (choice2fnsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compEex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionCommutes) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2W) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2A) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2B) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Equiv) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncInj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (leftInvIsSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjCantorThm) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (foundation2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSclos) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peano0notS) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peanoSinj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ordinalMinLem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (!!) @ (
% 121.77/16.27                                                                     ^[Y0 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (ordinal @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y1 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y2 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y2 @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ 
% 121.77/16.27                                                                      Y2) =>
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.27      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl45])).
% 121.77/16.27  thf(zip_derived_cl56, plain,
% 121.77/16.27      (~ (((descrp) =>
% 121.77/16.27           (((dsetconstrI) =>
% 121.77/16.27             (((dsetconstrEL) =>
% 121.77/16.27               (((dsetconstrER) =>
% 121.77/16.27                 (((exuE1) =>
% 121.77/16.27                   (((prop2setE) =>
% 121.77/16.27                     (((emptysetE) =>
% 121.77/16.27                       (((emptysetimpfalse) =>
% 121.77/16.27                         (((notinemptyset) =>
% 121.77/16.27                           (((exuE3e) =>
% 121.77/16.27                             (((setext) =>
% 121.77/16.27                               (((emptyI) =>
% 121.77/16.27                                 (((noeltsimpempty) =>
% 121.77/16.27                                   (((setbeta) =>
% 121.77/16.27                                     (((nonemptyE1) =>
% 121.77/16.27                                       (((nonemptyI) =>
% 121.77/16.27                                         (((nonemptyI1) =>
% 121.77/16.27                                           (((setadjoinIL) =>
% 121.77/16.27                                             (((in @ emptyset @ 
% 121.77/16.27                                               (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.27                                               (((setadjoinIR) =>
% 121.77/16.27                                                 (((setadjoinE) =>
% 121.77/16.27                                                   (((setadjoinOr) =>
% 121.77/16.27                                                     (((setoftrueEq) =>
% 121.77/16.27                                                       (((powersetI) =>
% 121.77/16.27                                                         (((emptyinPowerset) =>
% 121.77/16.27                                                           (((emptyInPowerset) =>
% 121.77/16.27                                                             (((powersetE) =>
% 121.77/16.27                                                               (((setunionI) =>
% 121.77/16.27                                                                 (((setunionE) =>
% 121.77/16.27                                                                   (((subPowSU) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (nonemptyImpWitness) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (uniqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsswitch) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptyE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (vacuousDall) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2setI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2set2propI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdexE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdallE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inCongP) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (in__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE3u) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exu__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoin__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powerset__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunion__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuEu) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (descr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dsetconstr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptysetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notsubsetI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetRefl) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTrans) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subset2powerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetemptysetimpeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepInPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2IR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (disjointsetsI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (bs114d) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusERneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusELneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusILneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusIRneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (secondinupair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairiskpair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsubunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairinpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsuniq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR11) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR12) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairequniteq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempaircEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrERa) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcImageSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (apProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (app) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (infuncsetfunc) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcinfuncset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcextLem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2lamEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrue) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueorfalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTELcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTERcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTnotintersectT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementImpComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contraSubsetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTcontraSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTILcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTIRcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTEcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule0) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1SetBreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (choice2fnsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compEex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionCommutes) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2W) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2A) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2B) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Equiv) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncInj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (leftInvIsSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjCantorThm) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (foundation2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSclos) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peano0notS) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peanoSinj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ordinalMinLem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (!!) @ (
% 121.77/16.27                                                                     ^[Y0 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (ordinal @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y1 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y2 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y2 @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ 
% 121.77/16.27                                                                      Y2) =>
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.27      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])).
% 121.77/16.27  thf(zip_derived_cl62, plain,
% 121.77/16.27      (~ (((dsetconstrI) =>
% 121.77/16.27           (((dsetconstrEL) =>
% 121.77/16.27             (((dsetconstrER) =>
% 121.77/16.27               (((exuE1) =>
% 121.77/16.27                 (((prop2setE) =>
% 121.77/16.27                   (((emptysetE) =>
% 121.77/16.27                     (((emptysetimpfalse) =>
% 121.77/16.27                       (((notinemptyset) =>
% 121.77/16.27                         (((exuE3e) =>
% 121.77/16.27                           (((setext) =>
% 121.77/16.27                             (((emptyI) =>
% 121.77/16.27                               (((noeltsimpempty) =>
% 121.77/16.27                                 (((setbeta) =>
% 121.77/16.27                                   (((nonemptyE1) =>
% 121.77/16.27                                     (((nonemptyI) =>
% 121.77/16.27                                       (((nonemptyI1) =>
% 121.77/16.27                                         (((setadjoinIL) =>
% 121.77/16.27                                           (((in @ emptyset @ 
% 121.77/16.27                                             (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.27                                             (((setadjoinIR) =>
% 121.77/16.27                                               (((setadjoinE) =>
% 121.77/16.27                                                 (((setadjoinOr) =>
% 121.77/16.27                                                   (((setoftrueEq) =>
% 121.77/16.27                                                     (((powersetI) =>
% 121.77/16.27                                                       (((emptyinPowerset) =>
% 121.77/16.27                                                         (((emptyInPowerset) =>
% 121.77/16.27                                                           (((powersetE) =>
% 121.77/16.27                                                             (((setunionI) =>
% 121.77/16.27                                                               (((setunionE) =>
% 121.77/16.27                                                                 (((subPowSU) =>
% 121.77/16.27                                                                   (((exuE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (nonemptyImpWitness) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (uniqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsswitch) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptyE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (vacuousDall) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2setI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2set2propI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdexE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdallE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inCongP) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (in__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE3u) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exu__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoin__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powerset__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunion__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuEu) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (descr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dsetconstr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptysetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notsubsetI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetRefl) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTrans) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subset2powerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetemptysetimpeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepInPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2IR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (disjointsetsI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (bs114d) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusERneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusELneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusILneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusIRneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (secondinupair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairiskpair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsubunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairinpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsuniq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR11) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR12) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairequniteq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempaircEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrERa) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcImageSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (apProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (app) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (infuncsetfunc) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcinfuncset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcextLem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2lamEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrue) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueorfalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTELcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTERcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTnotintersectT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementImpComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contraSubsetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTcontraSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTILcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTIRcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTEcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule0) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1SetBreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (choice2fnsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compEex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionCommutes) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2W) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2A) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2B) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Equiv) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncInj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (leftInvIsSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjCantorThm) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (foundation2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSclos) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peano0notS) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peanoSinj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ordinalMinLem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (!!) @ (
% 121.77/16.27                                                                     ^[Y0 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (ordinal @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y1 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y2 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y2 @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ 
% 121.77/16.27                                                                      Y2) =>
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.27      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl56])).
% 121.77/16.27  thf(zip_derived_cl69, plain,
% 121.77/16.27      (~ (((dsetconstrEL) =>
% 121.77/16.27           (((dsetconstrER) =>
% 121.77/16.27             (((exuE1) =>
% 121.77/16.27               (((prop2setE) =>
% 121.77/16.27                 (((emptysetE) =>
% 121.77/16.27                   (((emptysetimpfalse) =>
% 121.77/16.27                     (((notinemptyset) =>
% 121.77/16.27                       (((exuE3e) =>
% 121.77/16.27                         (((setext) =>
% 121.77/16.27                           (((emptyI) =>
% 121.77/16.27                             (((noeltsimpempty) =>
% 121.77/16.27                               (((setbeta) =>
% 121.77/16.27                                 (((nonemptyE1) =>
% 121.77/16.27                                   (((nonemptyI) =>
% 121.77/16.27                                     (((nonemptyI1) =>
% 121.77/16.27                                       (((setadjoinIL) =>
% 121.77/16.27                                         (((in @ emptyset @ 
% 121.77/16.27                                           (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.27                                           (((setadjoinIR) =>
% 121.77/16.27                                             (((setadjoinE) =>
% 121.77/16.27                                               (((setadjoinOr) =>
% 121.77/16.27                                                 (((setoftrueEq) =>
% 121.77/16.27                                                   (((powersetI) =>
% 121.77/16.27                                                     (((emptyinPowerset) =>
% 121.77/16.27                                                       (((emptyInPowerset) =>
% 121.77/16.27                                                         (((powersetE) =>
% 121.77/16.27                                                           (((setunionI) =>
% 121.77/16.27                                                             (((setunionE) =>
% 121.77/16.27                                                               (((subPowSU) =>
% 121.77/16.27                                                                 (((exuE2) =>
% 121.77/16.27                                                                   (((nonemptyImpWitness) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (uniqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsswitch) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptyE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (vacuousDall) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2setI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2set2propI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdexE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdallE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inCongP) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (in__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE3u) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exu__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoin__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powerset__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunion__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuEu) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (descr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dsetconstr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptysetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notsubsetI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetRefl) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTrans) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subset2powerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetemptysetimpeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepInPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2IR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (disjointsetsI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (bs114d) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusERneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusELneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusILneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusIRneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (secondinupair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairiskpair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsubunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairinpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1I2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsuniq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR11) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR12) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairequniteq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairinjR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ksndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairmemER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempaircEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodfstpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodsndpairEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairsurjEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrERa) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrEL2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dpsetconstrER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcImageSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (apProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (app) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (infuncsetfunc) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcinfuncset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamProp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lamp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2p) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (brelnall2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ex1E2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcextLem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcGraphProp4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (funcext2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ap2apEq2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (lam2lamEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (beta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eta2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalseProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueProp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifSingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ifp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (theeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrue) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iffalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (iftrueorfalse) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementT_lem) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTELcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectTERcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contrasubsetT3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (doubleComplementEq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTnotintersectT) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementImpComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (contraSubsetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementTcontraSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTILcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTIRcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionTEcontra) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2a) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2b) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (demorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule0) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz13rule4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz1_5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1SetBreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (choice2fnsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1all1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqbreln1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1invE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1compEex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionprop) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (breln1unionCommutes) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2W) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2A) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (woz2B) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Ex1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1Equiv) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (image1I) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (injFuncSetFuncInj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (leftInvIsSurj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (surjCantorThm) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (foundation2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinself2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (omegaSclos) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peano0notS) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (peanoSinj) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (transitivesetOp2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionTransitive) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ordinalMinLem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (!!) @ (
% 121.77/16.27                                                                     ^[Y0 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (ordinal @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y1 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (!!) @ (
% 121.77/16.27                                                                      ^[Y2 : $i]:
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y2 @ 
% 121.77/16.27                                                                      Y0) =>
% 121.77/16.27                                                                      ((
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ 
% 121.77/16.27                                                                      Y2) =>
% 121.77/16.27                                                                      (in @ 
% 121.77/16.27                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.27      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl62])).
% 121.77/16.27  thf(zip_derived_cl79, plain,
% 121.77/16.27      (~ (((dsetconstrER) =>
% 121.77/16.27           (((exuE1) =>
% 121.77/16.27             (((prop2setE) =>
% 121.77/16.27               (((emptysetE) =>
% 121.77/16.27                 (((emptysetimpfalse) =>
% 121.77/16.27                   (((notinemptyset) =>
% 121.77/16.27                     (((exuE3e) =>
% 121.77/16.27                       (((setext) =>
% 121.77/16.27                         (((emptyI) =>
% 121.77/16.27                           (((noeltsimpempty) =>
% 121.77/16.27                             (((setbeta) =>
% 121.77/16.27                               (((nonemptyE1) =>
% 121.77/16.27                                 (((nonemptyI) =>
% 121.77/16.27                                   (((nonemptyI1) =>
% 121.77/16.27                                     (((setadjoinIL) =>
% 121.77/16.27                                       (((in @ emptyset @ 
% 121.77/16.27                                         (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.27                                         (((setadjoinIR) =>
% 121.77/16.27                                           (((setadjoinE) =>
% 121.77/16.27                                             (((setadjoinOr) =>
% 121.77/16.27                                               (((setoftrueEq) =>
% 121.77/16.27                                                 (((powersetI) =>
% 121.77/16.27                                                   (((emptyinPowerset) =>
% 121.77/16.27                                                     (((emptyInPowerset) =>
% 121.77/16.27                                                       (((powersetE) =>
% 121.77/16.27                                                         (((setunionI) =>
% 121.77/16.27                                                           (((setunionE) =>
% 121.77/16.27                                                             (((subPowSU) =>
% 121.77/16.27                                                               (((exuE2) =>
% 121.77/16.27                                                                 (((nonemptyImpWitness) =>
% 121.77/16.27                                                                   (((uniqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notinsingleton) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqinunit) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsswitch) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsetIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptyE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (vacuousDall) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (quantDeMorgan4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2setI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (prop2set2propI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdexE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notdallE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inCongP) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (in__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuE3u) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exu__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoin__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powerset__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunion__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (exuEu) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (descr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (dsetconstr__Cong) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (eqimpsubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (emptysetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notsubsetI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (notequalI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetRefl) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetTrans) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setadjoinSub2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subset2powerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setextsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (subsetemptysetimpeq) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetE1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (inPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (powersetsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepInPowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (sepSubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2IR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionEcases) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binunionRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset5) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (disjointsetsI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectRsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset4) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (binintersectSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (bs114d) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusI) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusEL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusER) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusERneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusELneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusILneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusIRneg) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusLsub) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setminusSubset1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffE) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffI2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (symdiffIneg2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (secondinupair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIL) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setukpairIR) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairiskpair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (kpairp) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletonsubset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowerset) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (singletoninpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairset2E) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairsubunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (upairinpowunion) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (ubforcartprodlem3) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodpairin) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (cartprodmempair) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionE2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton1) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton2) =>
% 121.77/16.27                                                                     ((
% 121.77/16.27                                                                     (setunionsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsuniq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR11) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR12) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairequniteq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempaircEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrERa) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcImageSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (apProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (app) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (infuncsetfunc) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcinfuncset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcextLem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2lamEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrue) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueorfalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTELcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTERcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTnotintersectT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementImpComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contraSubsetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTcontraSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTILcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTIRcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTEcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule0) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1SetBreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (choice2fnsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compEex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionCommutes) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2W) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2A) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2B) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Equiv) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncInj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (leftInvIsSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjCantorThm) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (foundation2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSclos) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peano0notS) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peanoSinj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ordinalMinLem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (!!) @ (
% 121.77/16.28                                                                     ^[Y0 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (ordinal @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y1 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y2 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y2 @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ 
% 121.77/16.28                                                                      Y2) =>
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.28      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl69])).
% 121.77/16.28  thf(zip_derived_cl95, plain,
% 121.77/16.28      (~ (((exuE1) =>
% 121.77/16.28           (((prop2setE) =>
% 121.77/16.28             (((emptysetE) =>
% 121.77/16.28               (((emptysetimpfalse) =>
% 121.77/16.28                 (((notinemptyset) =>
% 121.77/16.28                   (((exuE3e) =>
% 121.77/16.28                     (((setext) =>
% 121.77/16.28                       (((emptyI) =>
% 121.77/16.28                         (((noeltsimpempty) =>
% 121.77/16.28                           (((setbeta) =>
% 121.77/16.28                             (((nonemptyE1) =>
% 121.77/16.28                               (((nonemptyI) =>
% 121.77/16.28                                 (((nonemptyI1) =>
% 121.77/16.28                                   (((setadjoinIL) =>
% 121.77/16.28                                     (((in @ emptyset @ 
% 121.77/16.28                                       (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.28                                       (((setadjoinIR) =>
% 121.77/16.28                                         (((setadjoinE) =>
% 121.77/16.28                                           (((setadjoinOr) =>
% 121.77/16.28                                             (((setoftrueEq) =>
% 121.77/16.28                                               (((powersetI) =>
% 121.77/16.28                                                 (((emptyinPowerset) =>
% 121.77/16.28                                                   (((emptyInPowerset) =>
% 121.77/16.28                                                     (((powersetE) =>
% 121.77/16.28                                                       (((setunionI) =>
% 121.77/16.28                                                         (((setunionE) =>
% 121.77/16.28                                                           (((subPowSU) =>
% 121.77/16.28                                                             (((exuE2) =>
% 121.77/16.28                                                               (((nonemptyImpWitness) =>
% 121.77/16.28                                                                 (((uniqinunit) =>
% 121.77/16.28                                                                   (((notinsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqinunit) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsswitch) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsetE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsetIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsetIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptyE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (vacuousDall) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2setI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2set2propI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdexE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdallE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inCongP) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (in__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuE3u) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exu__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoin__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powerset__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunion__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuEu) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (descr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dsetconstr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptysetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notsubsetI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetRefl) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTrans) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subset2powerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetemptysetimpeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepInPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2IR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (disjointsetsI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (bs114d) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusERneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusELneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusILneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusIRneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (secondinupair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairiskpair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsubunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairinpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsuniq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR11) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR12) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairequniteq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempaircEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrERa) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcImageSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (apProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (app) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (infuncsetfunc) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcinfuncset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcextLem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2lamEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrue) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueorfalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTELcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTERcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTnotintersectT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementImpComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contraSubsetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTcontraSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTILcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTIRcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTEcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule0) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1SetBreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (choice2fnsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compEex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionCommutes) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2W) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2A) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2B) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Equiv) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncInj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (leftInvIsSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjCantorThm) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (foundation2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSclos) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peano0notS) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peanoSinj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ordinalMinLem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (!!) @ (
% 121.77/16.28                                                                     ^[Y0 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (ordinal @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y1 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y2 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y2 @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ 
% 121.77/16.28                                                                      Y2) =>
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.28      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl79])).
% 121.77/16.28  thf(zip_derived_cl115, plain,
% 121.77/16.28      (~ (((prop2setE) =>
% 121.77/16.28           (((emptysetE) =>
% 121.77/16.28             (((emptysetimpfalse) =>
% 121.77/16.28               (((notinemptyset) =>
% 121.77/16.28                 (((exuE3e) =>
% 121.77/16.28                   (((setext) =>
% 121.77/16.28                     (((emptyI) =>
% 121.77/16.28                       (((noeltsimpempty) =>
% 121.77/16.28                         (((setbeta) =>
% 121.77/16.28                           (((nonemptyE1) =>
% 121.77/16.28                             (((nonemptyI) =>
% 121.77/16.28                               (((nonemptyI1) =>
% 121.77/16.28                                 (((setadjoinIL) =>
% 121.77/16.28                                   (((in @ emptyset @ 
% 121.77/16.28                                     (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.28                                     (((setadjoinIR) =>
% 121.77/16.28                                       (((setadjoinE) =>
% 121.77/16.28                                         (((setadjoinOr) =>
% 121.77/16.28                                           (((setoftrueEq) =>
% 121.77/16.28                                             (((powersetI) =>
% 121.77/16.28                                               (((emptyinPowerset) =>
% 121.77/16.28                                                 (((emptyInPowerset) =>
% 121.77/16.28                                                   (((powersetE) =>
% 121.77/16.28                                                     (((setunionI) =>
% 121.77/16.28                                                       (((setunionE) =>
% 121.77/16.28                                                         (((subPowSU) =>
% 121.77/16.28                                                           (((exuE2) =>
% 121.77/16.28                                                             (((nonemptyImpWitness) =>
% 121.77/16.28                                                               (((uniqinunit) =>
% 121.77/16.28                                                                 (((notinsingleton) =>
% 121.77/16.28                                                                   (((eqinunit) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsswitch) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsetE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsetIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsetIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptyE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (vacuousDall) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2setI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2set2propI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdexE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdallE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inCongP) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (in__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuE3u) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exu__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoin__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powerset__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunion__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuEu) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (descr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dsetconstr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptysetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notsubsetI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetRefl) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTrans) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subset2powerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetemptysetimpeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepInPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2IR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (disjointsetsI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (bs114d) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusERneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusELneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusILneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusIRneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (secondinupair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairiskpair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsubunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairinpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsuniq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR11) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR12) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairequniteq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempaircEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrERa) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcImageSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (apProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (app) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (infuncsetfunc) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcinfuncset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcextLem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2lamEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrue) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueorfalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTELcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTERcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTnotintersectT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementImpComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contraSubsetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTcontraSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTILcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTIRcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTEcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule0) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1SetBreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (choice2fnsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compEex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionCommutes) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2W) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2A) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2B) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Equiv) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncInj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (leftInvIsSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjCantorThm) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (foundation2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSclos) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peano0notS) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peanoSinj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ordinalMinLem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (!!) @ (
% 121.77/16.28                                                                     ^[Y0 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (ordinal @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y1 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y2 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y2 @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ 
% 121.77/16.28                                                                      Y2) =>
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.28      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl95])).
% 121.77/16.28  thf(zip_derived_cl133, plain,
% 121.77/16.28      (~ (((emptysetE) =>
% 121.77/16.28           (((emptysetimpfalse) =>
% 121.77/16.28             (((notinemptyset) =>
% 121.77/16.28               (((exuE3e) =>
% 121.77/16.28                 (((setext) =>
% 121.77/16.28                   (((emptyI) =>
% 121.77/16.28                     (((noeltsimpempty) =>
% 121.77/16.28                       (((setbeta) =>
% 121.77/16.28                         (((nonemptyE1) =>
% 121.77/16.28                           (((nonemptyI) =>
% 121.77/16.28                             (((nonemptyI1) =>
% 121.77/16.28                               (((setadjoinIL) =>
% 121.77/16.28                                 (((in @ emptyset @ 
% 121.77/16.28                                   (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.28                                   (((setadjoinIR) =>
% 121.77/16.28                                     (((setadjoinE) =>
% 121.77/16.28                                       (((setadjoinOr) =>
% 121.77/16.28                                         (((setoftrueEq) =>
% 121.77/16.28                                           (((powersetI) =>
% 121.77/16.28                                             (((emptyinPowerset) =>
% 121.77/16.28                                               (((emptyInPowerset) =>
% 121.77/16.28                                                 (((powersetE) =>
% 121.77/16.28                                                   (((setunionI) =>
% 121.77/16.28                                                     (((setunionE) =>
% 121.77/16.28                                                       (((subPowSU) =>
% 121.77/16.28                                                         (((exuE2) =>
% 121.77/16.28                                                           (((nonemptyImpWitness) =>
% 121.77/16.28                                                             (((uniqinunit) =>
% 121.77/16.28                                                               (((notinsingleton) =>
% 121.77/16.28                                                                 (((eqinunit) =>
% 121.77/16.28                                                                   (((singletonsswitch) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsetE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsetIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsetIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptyE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (vacuousDall) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2setI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2set2propI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdexE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdallE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inCongP) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (in__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuE3u) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exu__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoin__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powerset__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunion__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuEu) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (descr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dsetconstr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptysetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notsubsetI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetRefl) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTrans) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subset2powerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetemptysetimpeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepInPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2IR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (disjointsetsI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (bs114d) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusERneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusELneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusILneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusIRneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (secondinupair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairiskpair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsubunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairinpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsuniq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR11) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR12) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairequniteq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempaircEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrERa) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcImageSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (apProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (app) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (infuncsetfunc) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcinfuncset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcextLem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2lamEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrue) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueorfalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTELcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTERcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTnotintersectT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementImpComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contraSubsetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTcontraSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTILcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTIRcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTEcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule0) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1SetBreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (choice2fnsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compEex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionCommutes) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2W) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2A) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2B) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Equiv) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncInj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (leftInvIsSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjCantorThm) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (foundation2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSclos) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peano0notS) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peanoSinj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ordinalMinLem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (!!) @ (
% 121.77/16.28                                                                     ^[Y0 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (ordinal @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y1 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y2 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y2 @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ 
% 121.77/16.28                                                                      Y2) =>
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.28      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl115])).
% 121.77/16.28  thf(zip_derived_cl149, plain,
% 121.77/16.28      (~ (((emptysetimpfalse) =>
% 121.77/16.28           (((notinemptyset) =>
% 121.77/16.28             (((exuE3e) =>
% 121.77/16.28               (((setext) =>
% 121.77/16.28                 (((emptyI) =>
% 121.77/16.28                   (((noeltsimpempty) =>
% 121.77/16.28                     (((setbeta) =>
% 121.77/16.28                       (((nonemptyE1) =>
% 121.77/16.28                         (((nonemptyI) =>
% 121.77/16.28                           (((nonemptyI1) =>
% 121.77/16.28                             (((setadjoinIL) =>
% 121.77/16.28                               (((in @ emptyset @ 
% 121.77/16.28                                 (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.28                                 (((setadjoinIR) =>
% 121.77/16.28                                   (((setadjoinE) =>
% 121.77/16.28                                     (((setadjoinOr) =>
% 121.77/16.28                                       (((setoftrueEq) =>
% 121.77/16.28                                         (((powersetI) =>
% 121.77/16.28                                           (((emptyinPowerset) =>
% 121.77/16.28                                             (((emptyInPowerset) =>
% 121.77/16.28                                               (((powersetE) =>
% 121.77/16.28                                                 (((setunionI) =>
% 121.77/16.28                                                   (((setunionE) =>
% 121.77/16.28                                                     (((subPowSU) =>
% 121.77/16.28                                                       (((exuE2) =>
% 121.77/16.28                                                         (((nonemptyImpWitness) =>
% 121.77/16.28                                                           (((uniqinunit) =>
% 121.77/16.28                                                             (((notinsingleton) =>
% 121.77/16.28                                                               (((eqinunit) =>
% 121.77/16.28                                                                 (((singletonsswitch) =>
% 121.77/16.28                                                                   (((upairsetE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsetIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsetIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptyE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (vacuousDall) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2setI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2set2propI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdexE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdallE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inCongP) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (in__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuE3u) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exu__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoin__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powerset__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunion__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuEu) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (descr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dsetconstr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptysetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notsubsetI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetRefl) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTrans) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subset2powerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetemptysetimpeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepInPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2IR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (disjointsetsI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (bs114d) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusERneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusELneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusILneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusIRneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (secondinupair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairiskpair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsubunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairinpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsuniq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR11) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR12) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairequniteq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempaircEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrERa) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcImageSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (apProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (app) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (infuncsetfunc) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcinfuncset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcextLem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2lamEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrue) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueorfalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTELcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTERcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTnotintersectT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementImpComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contraSubsetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTcontraSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTILcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTIRcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTEcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule0) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1SetBreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (choice2fnsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compEex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionCommutes) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2W) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2A) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2B) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Equiv) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncInj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (leftInvIsSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjCantorThm) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (foundation2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSclos) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peano0notS) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peanoSinj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ordinalMinLem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (!!) @ (
% 121.77/16.28                                                                     ^[Y0 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (ordinal @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y1 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y2 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y2 @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ 
% 121.77/16.28                                                                      Y2) =>
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.28      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl133])).
% 121.77/16.28  thf(zip_derived_cl164, plain,
% 121.77/16.28      (~ (((notinemptyset) =>
% 121.77/16.28           (((exuE3e) =>
% 121.77/16.28             (((setext) =>
% 121.77/16.28               (((emptyI) =>
% 121.77/16.28                 (((noeltsimpempty) =>
% 121.77/16.28                   (((setbeta) =>
% 121.77/16.28                     (((nonemptyE1) =>
% 121.77/16.28                       (((nonemptyI) =>
% 121.77/16.28                         (((nonemptyI1) =>
% 121.77/16.28                           (((setadjoinIL) =>
% 121.77/16.28                             (((in @ emptyset @ 
% 121.77/16.28                               (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.28                               (((setadjoinIR) =>
% 121.77/16.28                                 (((setadjoinE) =>
% 121.77/16.28                                   (((setadjoinOr) =>
% 121.77/16.28                                     (((setoftrueEq) =>
% 121.77/16.28                                       (((powersetI) =>
% 121.77/16.28                                         (((emptyinPowerset) =>
% 121.77/16.28                                           (((emptyInPowerset) =>
% 121.77/16.28                                             (((powersetE) =>
% 121.77/16.28                                               (((setunionI) =>
% 121.77/16.28                                                 (((setunionE) =>
% 121.77/16.28                                                   (((subPowSU) =>
% 121.77/16.28                                                     (((exuE2) =>
% 121.77/16.28                                                       (((nonemptyImpWitness) =>
% 121.77/16.28                                                         (((uniqinunit) =>
% 121.77/16.28                                                           (((notinsingleton) =>
% 121.77/16.28                                                             (((eqinunit) =>
% 121.77/16.28                                                               (((singletonsswitch) =>
% 121.77/16.28                                                                 (((upairsetE) =>
% 121.77/16.28                                                                   (((upairsetIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsetIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptyE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (vacuousDall) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2setI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2set2propI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdexE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdallE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inCongP) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (in__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuE3u) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exu__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoin__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powerset__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunion__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuEu) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (descr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dsetconstr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptysetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notsubsetI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetRefl) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTrans) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subset2powerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetemptysetimpeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepInPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2IR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (disjointsetsI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (bs114d) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusERneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusELneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusILneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusIRneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (secondinupair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairiskpair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsubunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairinpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsuniq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR11) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR12) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairequniteq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempaircEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrERa) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcImageSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (apProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (app) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (infuncsetfunc) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcinfuncset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcextLem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2lamEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrue) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueorfalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTELcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTERcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTnotintersectT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementImpComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contraSubsetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTcontraSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTILcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTIRcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTEcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule0) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1SetBreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (choice2fnsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compEex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionCommutes) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2W) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2A) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2B) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Equiv) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncInj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (leftInvIsSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjCantorThm) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (foundation2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSclos) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peano0notS) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peanoSinj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ordinalMinLem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (!!) @ (
% 121.77/16.28                                                                     ^[Y0 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (ordinal @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y1 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y2 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y2 @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ 
% 121.77/16.28                                                                      Y2) =>
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.28      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl149])).
% 121.77/16.28  thf(zip_derived_cl177, plain,
% 121.77/16.28      (~ (((exuE3e) =>
% 121.77/16.28           (((setext) =>
% 121.77/16.28             (((emptyI) =>
% 121.77/16.28               (((noeltsimpempty) =>
% 121.77/16.28                 (((setbeta) =>
% 121.77/16.28                   (((nonemptyE1) =>
% 121.77/16.28                     (((nonemptyI) =>
% 121.77/16.28                       (((nonemptyI1) =>
% 121.77/16.28                         (((setadjoinIL) =>
% 121.77/16.28                           (((in @ emptyset @ 
% 121.77/16.28                             (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.28                             (((setadjoinIR) =>
% 121.77/16.28                               (((setadjoinE) =>
% 121.77/16.28                                 (((setadjoinOr) =>
% 121.77/16.28                                   (((setoftrueEq) =>
% 121.77/16.28                                     (((powersetI) =>
% 121.77/16.28                                       (((emptyinPowerset) =>
% 121.77/16.28                                         (((emptyInPowerset) =>
% 121.77/16.28                                           (((powersetE) =>
% 121.77/16.28                                             (((setunionI) =>
% 121.77/16.28                                               (((setunionE) =>
% 121.77/16.28                                                 (((subPowSU) =>
% 121.77/16.28                                                   (((exuE2) =>
% 121.77/16.28                                                     (((nonemptyImpWitness) =>
% 121.77/16.28                                                       (((uniqinunit) =>
% 121.77/16.28                                                         (((notinsingleton) =>
% 121.77/16.28                                                           (((eqinunit) =>
% 121.77/16.28                                                             (((singletonsswitch) =>
% 121.77/16.28                                                               (((upairsetE) =>
% 121.77/16.28                                                                 (((upairsetIL) =>
% 121.77/16.28                                                                   (((upairsetIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptyE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (vacuousDall) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2setI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2set2propI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdexE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdallE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inCongP) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (in__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuE3u) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exu__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoin__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powerset__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunion__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuEu) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (descr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dsetconstr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptysetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notsubsetI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetRefl) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTrans) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subset2powerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetemptysetimpeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepInPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2IR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (disjointsetsI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (bs114d) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusERneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusELneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusILneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusIRneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (secondinupair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairiskpair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsubunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairinpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsuniq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR11) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR12) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairequniteq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempaircEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrERa) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcImageSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (apProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (app) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (infuncsetfunc) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcinfuncset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcextLem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2lamEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrue) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueorfalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTELcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTERcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTnotintersectT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementImpComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contraSubsetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTcontraSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTILcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTIRcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTEcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule0) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1SetBreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (choice2fnsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compEex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionCommutes) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2W) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2A) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2B) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Equiv) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncInj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (leftInvIsSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjCantorThm) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (foundation2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSclos) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peano0notS) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peanoSinj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ordinalMinLem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (!!) @ (
% 121.77/16.28                                                                     ^[Y0 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (ordinal @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y1 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y2 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y2 @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ 
% 121.77/16.28                                                                      Y2) =>
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.28      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl164])).
% 121.77/16.28  thf(zip_derived_cl191, plain,
% 121.77/16.28      (~ (((setext) =>
% 121.77/16.28           (((emptyI) =>
% 121.77/16.28             (((noeltsimpempty) =>
% 121.77/16.28               (((setbeta) =>
% 121.77/16.28                 (((nonemptyE1) =>
% 121.77/16.28                   (((nonemptyI) =>
% 121.77/16.28                     (((nonemptyI1) =>
% 121.77/16.28                       (((setadjoinIL) =>
% 121.77/16.28                         (((in @ emptyset @ 
% 121.77/16.28                           (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.28                           (((setadjoinIR) =>
% 121.77/16.28                             (((setadjoinE) =>
% 121.77/16.28                               (((setadjoinOr) =>
% 121.77/16.28                                 (((setoftrueEq) =>
% 121.77/16.28                                   (((powersetI) =>
% 121.77/16.28                                     (((emptyinPowerset) =>
% 121.77/16.28                                       (((emptyInPowerset) =>
% 121.77/16.28                                         (((powersetE) =>
% 121.77/16.28                                           (((setunionI) =>
% 121.77/16.28                                             (((setunionE) =>
% 121.77/16.28                                               (((subPowSU) =>
% 121.77/16.28                                                 (((exuE2) =>
% 121.77/16.28                                                   (((nonemptyImpWitness) =>
% 121.77/16.28                                                     (((uniqinunit) =>
% 121.77/16.28                                                       (((notinsingleton) =>
% 121.77/16.28                                                         (((eqinunit) =>
% 121.77/16.28                                                           (((singletonsswitch) =>
% 121.77/16.28                                                             (((upairsetE) =>
% 121.77/16.28                                                               (((upairsetIL) =>
% 121.77/16.28                                                                 (((upairsetIR) =>
% 121.77/16.28                                                                   (((emptyE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (vacuousDall) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2setI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2set2propI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdexE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdallE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inCongP) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (in__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuE3u) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exu__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoin__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powerset__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunion__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuEu) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (descr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dsetconstr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptysetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notsubsetI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetRefl) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTrans) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subset2powerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetemptysetimpeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepInPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2IR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (disjointsetsI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (bs114d) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusERneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusELneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusILneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusIRneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (secondinupair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairiskpair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsubunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairinpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsuniq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR11) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR12) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairequniteq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempaircEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrERa) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrEL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcImageSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (apProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (app) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (infuncsetfunc) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcinfuncset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamProp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lamp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2p) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (brelnall2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcextLem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcGraphProp4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (funcext2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ap2apEq2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (lam2lamEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (beta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eta2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalseProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueProp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifSingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ifp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrue) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iffalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (iftrueorfalse) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementT_lem) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTELcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectTERcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contrasubsetT3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (doubleComplementEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTnotintersectT) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementImpComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (contraSubsetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementTcontraSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTILcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTIRcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionTEcontra) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2a) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2b) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (demorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule0) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz13rule4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz1_5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1SetBreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (choice2fnsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1all1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqbreln1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1invE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1compEex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (breln1unionCommutes) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2W) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2A) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (woz2B) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Ex1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1Equiv) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (image1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (injFuncSetFuncInj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (leftInvIsSurj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (surjCantorThm) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (foundation2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notinself2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (omegaSclos) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peano0notS) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (peanoSinj) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (transitivesetOp2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionTransitive) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ordinalMinLem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (!!) @ (
% 121.77/16.28                                                                     ^[Y0 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (ordinal @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y1 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (!!) @ (
% 121.77/16.28                                                                      ^[Y2 : $i]:
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y2 @ 
% 121.77/16.28                                                                      Y0) =>
% 121.77/16.28                                                                      ((
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ 
% 121.77/16.28                                                                      Y2) =>
% 121.77/16.28                                                                      (in @ 
% 121.77/16.28                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.28      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl177])).
% 121.77/16.28  thf(zip_derived_cl205, plain,
% 121.77/16.28      (~ (((emptyI) =>
% 121.77/16.28           (((noeltsimpempty) =>
% 121.77/16.28             (((setbeta) =>
% 121.77/16.28               (((nonemptyE1) =>
% 121.77/16.28                 (((nonemptyI) =>
% 121.77/16.28                   (((nonemptyI1) =>
% 121.77/16.28                     (((setadjoinIL) =>
% 121.77/16.28                       (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.28                         (((setadjoinIR) =>
% 121.77/16.28                           (((setadjoinE) =>
% 121.77/16.28                             (((setadjoinOr) =>
% 121.77/16.28                               (((setoftrueEq) =>
% 121.77/16.28                                 (((powersetI) =>
% 121.77/16.28                                   (((emptyinPowerset) =>
% 121.77/16.28                                     (((emptyInPowerset) =>
% 121.77/16.28                                       (((powersetE) =>
% 121.77/16.28                                         (((setunionI) =>
% 121.77/16.28                                           (((setunionE) =>
% 121.77/16.28                                             (((subPowSU) =>
% 121.77/16.28                                               (((exuE2) =>
% 121.77/16.28                                                 (((nonemptyImpWitness) =>
% 121.77/16.28                                                   (((uniqinunit) =>
% 121.77/16.28                                                     (((notinsingleton) =>
% 121.77/16.28                                                       (((eqinunit) =>
% 121.77/16.28                                                         (((singletonsswitch) =>
% 121.77/16.28                                                           (((upairsetE) =>
% 121.77/16.28                                                             (((upairsetIL) =>
% 121.77/16.28                                                               (((upairsetIR) =>
% 121.77/16.28                                                                 (((emptyE1) =>
% 121.77/16.28                                                                   (((vacuousDall) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (quantDeMorgan4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2setI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (prop2set2propI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdexE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notdallE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inCongP) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (in__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuE3u) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exu__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoin__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powerset__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunion__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (exuEu) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (descr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dsetconstr__Cong) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (eqimpsubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (emptysetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notsubsetI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (notequalI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetRefl) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetTrans) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setadjoinSub2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subset2powerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setextsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (subsetemptysetimpeq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetE1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (inPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (powersetsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepInPowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (sepSubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2IR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionEcases) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binunionRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset5) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (disjointsetsI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectRsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset4) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (binintersectSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (bs114d) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusERneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusELneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusILneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusIRneg) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusLsub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setminusSubset1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffE) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffI2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (symdiffIneg2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (secondinupair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairIR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairiskpair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairp) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsubset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowerset) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletoninpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairset2E) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairsubunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairinpowunion) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ubforcartprodlem3) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempair) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionE2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setunionsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1E1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ex1I2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (singletonsuniq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (theprop) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR11) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR12) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR1) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (upairequniteq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR2) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (setukpairinjR) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndsingleton) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (ksndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (kpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndin) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemEL) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairmemER) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodmempaircEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodfstpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodsndpairEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (cartprodpairsurjEq) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrI) =>
% 121.77/16.28                                                                     ((
% 121.77/16.28                                                                     (dpsetconstrSub) =>
% 121.77/16.28                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrERa) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcImageSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (apProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (app) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (infuncsetfunc) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcinfuncset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcextLem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2lamEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrue) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueorfalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTELcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTERcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTnotintersectT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementImpComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contraSubsetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTcontraSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTILcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTIRcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTEcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule0) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1SetBreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (choice2fnsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compEex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionCommutes) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2W) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2A) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2B) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Equiv) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncInj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (leftInvIsSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjCantorThm) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (foundation2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSclos) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peano0notS) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peanoSinj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ordinalMinLem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (!!) @ (
% 121.77/16.29                                                                     ^[Y0 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (ordinal @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y1 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y2 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y2 @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ 
% 121.77/16.29                                                                      Y2) =>
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.29      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl191])).
% 121.77/16.29  thf(zip_derived_cl219, plain,
% 121.77/16.29      (~ (((noeltsimpempty) =>
% 121.77/16.29           (((setbeta) =>
% 121.77/16.29             (((nonemptyE1) =>
% 121.77/16.29               (((nonemptyI) =>
% 121.77/16.29                 (((nonemptyI1) =>
% 121.77/16.29                   (((setadjoinIL) =>
% 121.77/16.29                     (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.29                       (((setadjoinIR) =>
% 121.77/16.29                         (((setadjoinE) =>
% 121.77/16.29                           (((setadjoinOr) =>
% 121.77/16.29                             (((setoftrueEq) =>
% 121.77/16.29                               (((powersetI) =>
% 121.77/16.29                                 (((emptyinPowerset) =>
% 121.77/16.29                                   (((emptyInPowerset) =>
% 121.77/16.29                                     (((powersetE) =>
% 121.77/16.29                                       (((setunionI) =>
% 121.77/16.29                                         (((setunionE) =>
% 121.77/16.29                                           (((subPowSU) =>
% 121.77/16.29                                             (((exuE2) =>
% 121.77/16.29                                               (((nonemptyImpWitness) =>
% 121.77/16.29                                                 (((uniqinunit) =>
% 121.77/16.29                                                   (((notinsingleton) =>
% 121.77/16.29                                                     (((eqinunit) =>
% 121.77/16.29                                                       (((singletonsswitch) =>
% 121.77/16.29                                                         (((upairsetE) =>
% 121.77/16.29                                                           (((upairsetIL) =>
% 121.77/16.29                                                             (((upairsetIR) =>
% 121.77/16.29                                                               (((emptyE1) =>
% 121.77/16.29                                                                 (((vacuousDall) =>
% 121.77/16.29                                                                   (((quantDeMorgan1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (quantDeMorgan2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (quantDeMorgan3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (quantDeMorgan4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (prop2setI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (prop2set2propI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdexE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdallE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inCongP) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (in__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuE3u) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exu__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoin__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powerset__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunion__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuEu) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (descr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dsetconstr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (emptysetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notsubsetI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetRefl) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTrans) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subset2powerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetemptysetimpeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepInPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2IR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (disjointsetsI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (bs114d) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusERneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusELneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusILneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusIRneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (secondinupair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairiskpair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairsubunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairinpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsuniq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR11) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR12) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairequniteq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempaircEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrERa) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcImageSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (apProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (app) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (infuncsetfunc) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcinfuncset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcextLem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2lamEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrue) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueorfalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTELcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTERcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTnotintersectT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementImpComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contraSubsetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTcontraSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTILcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTIRcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTEcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule0) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1SetBreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (choice2fnsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compEex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionCommutes) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2W) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2A) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2B) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Equiv) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncInj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (leftInvIsSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjCantorThm) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (foundation2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSclos) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peano0notS) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peanoSinj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ordinalMinLem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (!!) @ (
% 121.77/16.29                                                                     ^[Y0 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (ordinal @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y1 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y2 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y2 @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ 
% 121.77/16.29                                                                      Y2) =>
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.29      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl205])).
% 121.77/16.29  thf(zip_derived_cl231, plain,
% 121.77/16.29      (~ (((setbeta) =>
% 121.77/16.29           (((nonemptyE1) =>
% 121.77/16.29             (((nonemptyI) =>
% 121.77/16.29               (((nonemptyI1) =>
% 121.77/16.29                 (((setadjoinIL) =>
% 121.77/16.29                   (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.29                     (((setadjoinIR) =>
% 121.77/16.29                       (((setadjoinE) =>
% 121.77/16.29                         (((setadjoinOr) =>
% 121.77/16.29                           (((setoftrueEq) =>
% 121.77/16.29                             (((powersetI) =>
% 121.77/16.29                               (((emptyinPowerset) =>
% 121.77/16.29                                 (((emptyInPowerset) =>
% 121.77/16.29                                   (((powersetE) =>
% 121.77/16.29                                     (((setunionI) =>
% 121.77/16.29                                       (((setunionE) =>
% 121.77/16.29                                         (((subPowSU) =>
% 121.77/16.29                                           (((exuE2) =>
% 121.77/16.29                                             (((nonemptyImpWitness) =>
% 121.77/16.29                                               (((uniqinunit) =>
% 121.77/16.29                                                 (((notinsingleton) =>
% 121.77/16.29                                                   (((eqinunit) =>
% 121.77/16.29                                                     (((singletonsswitch) =>
% 121.77/16.29                                                       (((upairsetE) =>
% 121.77/16.29                                                         (((upairsetIL) =>
% 121.77/16.29                                                           (((upairsetIR) =>
% 121.77/16.29                                                             (((emptyE1) =>
% 121.77/16.29                                                               (((vacuousDall) =>
% 121.77/16.29                                                                 (((quantDeMorgan1) =>
% 121.77/16.29                                                                   (((quantDeMorgan2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (quantDeMorgan3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (quantDeMorgan4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (prop2setI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (prop2set2propI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdexE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdallE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inCongP) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (in__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuE3u) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exu__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoin__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powerset__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunion__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuEu) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (descr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dsetconstr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (emptysetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notsubsetI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetRefl) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTrans) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subset2powerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetemptysetimpeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepInPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2IR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (disjointsetsI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (bs114d) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusERneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusELneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusILneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusIRneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (secondinupair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairiskpair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairsubunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairinpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsuniq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR11) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR12) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairequniteq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempaircEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrERa) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcImageSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (apProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (app) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (infuncsetfunc) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcinfuncset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcextLem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2lamEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrue) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueorfalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTELcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTERcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTnotintersectT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementImpComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contraSubsetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTcontraSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTILcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTIRcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTEcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule0) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1SetBreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (choice2fnsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compEex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionCommutes) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2W) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2A) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2B) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Equiv) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncInj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (leftInvIsSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjCantorThm) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (foundation2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSclos) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peano0notS) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peanoSinj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ordinalMinLem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (!!) @ (
% 121.77/16.29                                                                     ^[Y0 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (ordinal @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y1 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y2 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y2 @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ 
% 121.77/16.29                                                                      Y2) =>
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.29      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl219])).
% 121.77/16.29  thf(zip_derived_cl244, plain,
% 121.77/16.29      (~ (((nonemptyE1) =>
% 121.77/16.29           (((nonemptyI) =>
% 121.77/16.29             (((nonemptyI1) =>
% 121.77/16.29               (((setadjoinIL) =>
% 121.77/16.29                 (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.29                   (((setadjoinIR) =>
% 121.77/16.29                     (((setadjoinE) =>
% 121.77/16.29                       (((setadjoinOr) =>
% 121.77/16.29                         (((setoftrueEq) =>
% 121.77/16.29                           (((powersetI) =>
% 121.77/16.29                             (((emptyinPowerset) =>
% 121.77/16.29                               (((emptyInPowerset) =>
% 121.77/16.29                                 (((powersetE) =>
% 121.77/16.29                                   (((setunionI) =>
% 121.77/16.29                                     (((setunionE) =>
% 121.77/16.29                                       (((subPowSU) =>
% 121.77/16.29                                         (((exuE2) =>
% 121.77/16.29                                           (((nonemptyImpWitness) =>
% 121.77/16.29                                             (((uniqinunit) =>
% 121.77/16.29                                               (((notinsingleton) =>
% 121.77/16.29                                                 (((eqinunit) =>
% 121.77/16.29                                                   (((singletonsswitch) =>
% 121.77/16.29                                                     (((upairsetE) =>
% 121.77/16.29                                                       (((upairsetIL) =>
% 121.77/16.29                                                         (((upairsetIR) =>
% 121.77/16.29                                                           (((emptyE1) =>
% 121.77/16.29                                                             (((vacuousDall) =>
% 121.77/16.29                                                               (((quantDeMorgan1) =>
% 121.77/16.29                                                                 (((quantDeMorgan2) =>
% 121.77/16.29                                                                   (((quantDeMorgan3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (quantDeMorgan4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (prop2setI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (prop2set2propI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdexE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdallE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inCongP) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (in__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuE3u) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exu__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoin__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powerset__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunion__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuEu) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (descr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dsetconstr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (emptysetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notsubsetI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetRefl) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTrans) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subset2powerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetemptysetimpeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepInPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2IR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (disjointsetsI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (bs114d) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusERneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusELneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusILneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusIRneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (secondinupair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairiskpair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairsubunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairinpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsuniq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR11) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR12) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairequniteq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempaircEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrERa) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcImageSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (apProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (app) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (infuncsetfunc) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcinfuncset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcextLem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2lamEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrue) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueorfalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTELcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTERcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTnotintersectT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementImpComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contraSubsetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTcontraSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTILcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTIRcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTEcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule0) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1SetBreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (choice2fnsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compEex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionCommutes) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2W) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2A) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2B) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Equiv) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncInj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (leftInvIsSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjCantorThm) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (foundation2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSclos) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peano0notS) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peanoSinj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ordinalMinLem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (!!) @ (
% 121.77/16.29                                                                     ^[Y0 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (ordinal @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y1 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y2 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y2 @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ 
% 121.77/16.29                                                                      Y2) =>
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.29      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl231])).
% 121.77/16.29  thf(zip_derived_cl258, plain,
% 121.77/16.29      (~ (((nonemptyI) =>
% 121.77/16.29           (((nonemptyI1) =>
% 121.77/16.29             (((setadjoinIL) =>
% 121.77/16.29               (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.29                 (((setadjoinIR) =>
% 121.77/16.29                   (((setadjoinE) =>
% 121.77/16.29                     (((setadjoinOr) =>
% 121.77/16.29                       (((setoftrueEq) =>
% 121.77/16.29                         (((powersetI) =>
% 121.77/16.29                           (((emptyinPowerset) =>
% 121.77/16.29                             (((emptyInPowerset) =>
% 121.77/16.29                               (((powersetE) =>
% 121.77/16.29                                 (((setunionI) =>
% 121.77/16.29                                   (((setunionE) =>
% 121.77/16.29                                     (((subPowSU) =>
% 121.77/16.29                                       (((exuE2) =>
% 121.77/16.29                                         (((nonemptyImpWitness) =>
% 121.77/16.29                                           (((uniqinunit) =>
% 121.77/16.29                                             (((notinsingleton) =>
% 121.77/16.29                                               (((eqinunit) =>
% 121.77/16.29                                                 (((singletonsswitch) =>
% 121.77/16.29                                                   (((upairsetE) =>
% 121.77/16.29                                                     (((upairsetIL) =>
% 121.77/16.29                                                       (((upairsetIR) =>
% 121.77/16.29                                                         (((emptyE1) =>
% 121.77/16.29                                                           (((vacuousDall) =>
% 121.77/16.29                                                             (((quantDeMorgan1) =>
% 121.77/16.29                                                               (((quantDeMorgan2) =>
% 121.77/16.29                                                                 (((quantDeMorgan3) =>
% 121.77/16.29                                                                   (((quantDeMorgan4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (prop2setI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (prop2set2propI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdexE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdallE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inCongP) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (in__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuE3u) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exu__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoin__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powerset__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunion__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuEu) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (descr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dsetconstr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (emptysetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notsubsetI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetRefl) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTrans) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subset2powerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetemptysetimpeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepInPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2IR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (disjointsetsI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (bs114d) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusERneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusELneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusILneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusIRneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (secondinupair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairiskpair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairsubunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairinpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsuniq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR11) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR12) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairequniteq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempaircEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrERa) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcImageSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (apProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (app) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (infuncsetfunc) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcinfuncset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcextLem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2lamEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrue) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueorfalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTELcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTERcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTnotintersectT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementImpComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contraSubsetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTcontraSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTILcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTIRcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTEcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule0) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1SetBreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (choice2fnsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compEex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionCommutes) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2W) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2A) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2B) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Equiv) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncInj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (leftInvIsSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjCantorThm) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (foundation2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSclos) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peano0notS) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peanoSinj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ordinalMinLem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (!!) @ (
% 121.77/16.29                                                                     ^[Y0 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (ordinal @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y1 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y2 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y2 @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ 
% 121.77/16.29                                                                      Y2) =>
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.29      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl244])).
% 121.77/16.29  thf(zip_derived_cl274, plain,
% 121.77/16.29      (~ (((nonemptyI1) =>
% 121.77/16.29           (((setadjoinIL) =>
% 121.77/16.29             (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.29               (((setadjoinIR) =>
% 121.77/16.29                 (((setadjoinE) =>
% 121.77/16.29                   (((setadjoinOr) =>
% 121.77/16.29                     (((setoftrueEq) =>
% 121.77/16.29                       (((powersetI) =>
% 121.77/16.29                         (((emptyinPowerset) =>
% 121.77/16.29                           (((emptyInPowerset) =>
% 121.77/16.29                             (((powersetE) =>
% 121.77/16.29                               (((setunionI) =>
% 121.77/16.29                                 (((setunionE) =>
% 121.77/16.29                                   (((subPowSU) =>
% 121.77/16.29                                     (((exuE2) =>
% 121.77/16.29                                       (((nonemptyImpWitness) =>
% 121.77/16.29                                         (((uniqinunit) =>
% 121.77/16.29                                           (((notinsingleton) =>
% 121.77/16.29                                             (((eqinunit) =>
% 121.77/16.29                                               (((singletonsswitch) =>
% 121.77/16.29                                                 (((upairsetE) =>
% 121.77/16.29                                                   (((upairsetIL) =>
% 121.77/16.29                                                     (((upairsetIR) =>
% 121.77/16.29                                                       (((emptyE1) =>
% 121.77/16.29                                                         (((vacuousDall) =>
% 121.77/16.29                                                           (((quantDeMorgan1) =>
% 121.77/16.29                                                             (((quantDeMorgan2) =>
% 121.77/16.29                                                               (((quantDeMorgan3) =>
% 121.77/16.29                                                                 (((quantDeMorgan4) =>
% 121.77/16.29                                                                   (((prop2setI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (prop2set2propI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdexE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdallE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inCongP) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (in__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuE3u) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exu__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoin__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powerset__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunion__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuEu) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (descr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dsetconstr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (emptysetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notsubsetI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetRefl) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTrans) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subset2powerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetemptysetimpeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepInPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2IR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (disjointsetsI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (bs114d) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusERneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusELneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusILneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusIRneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (secondinupair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairiskpair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairsubunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairinpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsuniq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR11) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR12) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairequniteq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempaircEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrERa) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcImageSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (apProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (app) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (infuncsetfunc) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcinfuncset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcextLem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2lamEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrue) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueorfalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTELcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTERcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTnotintersectT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementImpComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contraSubsetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTcontraSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTILcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTIRcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTEcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule0) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1SetBreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (choice2fnsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compEex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionCommutes) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2W) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2A) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2B) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Equiv) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncInj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (leftInvIsSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjCantorThm) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (foundation2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSclos) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peano0notS) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peanoSinj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ordinalMinLem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (!!) @ (
% 121.77/16.29                                                                     ^[Y0 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (ordinal @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y1 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y2 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y2 @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ 
% 121.77/16.29                                                                      Y2) =>
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.29      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl258])).
% 121.77/16.29  thf(zip_derived_cl285, plain,
% 121.77/16.29      (~ (((setadjoinIL) =>
% 121.77/16.29           (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.29             (((setadjoinIR) =>
% 121.77/16.29               (((setadjoinE) =>
% 121.77/16.29                 (((setadjoinOr) =>
% 121.77/16.29                   (((setoftrueEq) =>
% 121.77/16.29                     (((powersetI) =>
% 121.77/16.29                       (((emptyinPowerset) =>
% 121.77/16.29                         (((emptyInPowerset) =>
% 121.77/16.29                           (((powersetE) =>
% 121.77/16.29                             (((setunionI) =>
% 121.77/16.29                               (((setunionE) =>
% 121.77/16.29                                 (((subPowSU) =>
% 121.77/16.29                                   (((exuE2) =>
% 121.77/16.29                                     (((nonemptyImpWitness) =>
% 121.77/16.29                                       (((uniqinunit) =>
% 121.77/16.29                                         (((notinsingleton) =>
% 121.77/16.29                                           (((eqinunit) =>
% 121.77/16.29                                             (((singletonsswitch) =>
% 121.77/16.29                                               (((upairsetE) =>
% 121.77/16.29                                                 (((upairsetIL) =>
% 121.77/16.29                                                   (((upairsetIR) =>
% 121.77/16.29                                                     (((emptyE1) =>
% 121.77/16.29                                                       (((vacuousDall) =>
% 121.77/16.29                                                         (((quantDeMorgan1) =>
% 121.77/16.29                                                           (((quantDeMorgan2) =>
% 121.77/16.29                                                             (((quantDeMorgan3) =>
% 121.77/16.29                                                               (((quantDeMorgan4) =>
% 121.77/16.29                                                                 (((prop2setI) =>
% 121.77/16.29                                                                   (((prop2set2propI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdexE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdallE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inCongP) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (in__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuE3u) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exu__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoin__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powerset__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunion__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuEu) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (descr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dsetconstr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (emptysetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notsubsetI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetRefl) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTrans) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subset2powerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetemptysetimpeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepInPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2IR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (disjointsetsI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (bs114d) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusERneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusELneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusILneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusIRneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (secondinupair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairiskpair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairsubunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairinpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsuniq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR11) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR12) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairequniteq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempaircEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrERa) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcImageSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (apProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (app) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (infuncsetfunc) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcinfuncset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcextLem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2lamEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrue) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueorfalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTELcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTERcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTnotintersectT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementImpComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contraSubsetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTcontraSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTILcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTIRcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTEcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule0) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1SetBreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (choice2fnsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compEex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionCommutes) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2W) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2A) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2B) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Equiv) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncInj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (leftInvIsSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjCantorThm) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (foundation2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSclos) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peano0notS) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peanoSinj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ordinalMinLem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (!!) @ (
% 121.77/16.29                                                                     ^[Y0 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (ordinal @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y1 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y2 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y2 @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ 
% 121.77/16.29                                                                      Y2) =>
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.29      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl274])).
% 121.77/16.29  thf(zip_derived_cl297, plain,
% 121.77/16.29      (~ (((in @ emptyset @ (setadjoin @ emptyset @ emptyset)) =>
% 121.77/16.29           (((setadjoinIR) =>
% 121.77/16.29             (((setadjoinE) =>
% 121.77/16.29               (((setadjoinOr) =>
% 121.77/16.29                 (((setoftrueEq) =>
% 121.77/16.29                   (((powersetI) =>
% 121.77/16.29                     (((emptyinPowerset) =>
% 121.77/16.29                       (((emptyInPowerset) =>
% 121.77/16.29                         (((powersetE) =>
% 121.77/16.29                           (((setunionI) =>
% 121.77/16.29                             (((setunionE) =>
% 121.77/16.29                               (((subPowSU) =>
% 121.77/16.29                                 (((exuE2) =>
% 121.77/16.29                                   (((nonemptyImpWitness) =>
% 121.77/16.29                                     (((uniqinunit) =>
% 121.77/16.29                                       (((notinsingleton) =>
% 121.77/16.29                                         (((eqinunit) =>
% 121.77/16.29                                           (((singletonsswitch) =>
% 121.77/16.29                                             (((upairsetE) =>
% 121.77/16.29                                               (((upairsetIL) =>
% 121.77/16.29                                                 (((upairsetIR) =>
% 121.77/16.29                                                   (((emptyE1) =>
% 121.77/16.29                                                     (((vacuousDall) =>
% 121.77/16.29                                                       (((quantDeMorgan1) =>
% 121.77/16.29                                                         (((quantDeMorgan2) =>
% 121.77/16.29                                                           (((quantDeMorgan3) =>
% 121.77/16.29                                                             (((quantDeMorgan4) =>
% 121.77/16.29                                                               (((prop2setI) =>
% 121.77/16.29                                                                 (((prop2set2propI) =>
% 121.77/16.29                                                                   (((notdexE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notdallE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inCongP) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (in__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuE3u) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exu__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoin__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powerset__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunion__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuEu) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (descr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dsetconstr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (emptysetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notsubsetI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetRefl) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTrans) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subset2powerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetemptysetimpeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepInPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2IR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (disjointsetsI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (bs114d) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusERneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusELneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusILneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusIRneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (secondinupair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairiskpair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairsubunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairinpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsuniq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR11) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR12) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairequniteq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempaircEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrERa) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcImageSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (apProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (app) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (infuncsetfunc) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcinfuncset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcextLem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2lamEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrue) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueorfalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTELcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTERcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTnotintersectT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementImpComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contraSubsetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTcontraSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTILcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTIRcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTEcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule0) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1SetBreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (choice2fnsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1compEex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1unionCommutes) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2W) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2A) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz2B) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Ex1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1Equiv) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (image1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (injFuncSetFuncInj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (leftInvIsSurj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (surjCantorThm) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (foundation2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notinself2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (omegaSclos) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peano0notS) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (peanoSinj) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (transitivesetOp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionTransitive) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ordinalMinLem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (!!) @ (
% 121.77/16.29                                                                     ^[Y0 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (ordinal @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y1 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (!!) @ (
% 121.77/16.29                                                                      ^[Y2 : $i]:
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y2 @ 
% 121.77/16.29                                                                      Y0) =>
% 121.77/16.29                                                                      ((
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ 
% 121.77/16.29                                                                      Y2) =>
% 121.77/16.29                                                                      (in @ 
% 121.77/16.29                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.29      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl285])).
% 121.77/16.29  thf(zip_derived_cl305, plain,
% 121.77/16.29      (~ (((setadjoinIR) =>
% 121.77/16.29           (((setadjoinE) =>
% 121.77/16.29             (((setadjoinOr) =>
% 121.77/16.29               (((setoftrueEq) =>
% 121.77/16.29                 (((powersetI) =>
% 121.77/16.29                   (((emptyinPowerset) =>
% 121.77/16.29                     (((emptyInPowerset) =>
% 121.77/16.29                       (((powersetE) =>
% 121.77/16.29                         (((setunionI) =>
% 121.77/16.29                           (((setunionE) =>
% 121.77/16.29                             (((subPowSU) =>
% 121.77/16.29                               (((exuE2) =>
% 121.77/16.29                                 (((nonemptyImpWitness) =>
% 121.77/16.29                                   (((uniqinunit) =>
% 121.77/16.29                                     (((notinsingleton) =>
% 121.77/16.29                                       (((eqinunit) =>
% 121.77/16.29                                         (((singletonsswitch) =>
% 121.77/16.29                                           (((upairsetE) =>
% 121.77/16.29                                             (((upairsetIL) =>
% 121.77/16.29                                               (((upairsetIR) =>
% 121.77/16.29                                                 (((emptyE1) =>
% 121.77/16.29                                                   (((vacuousDall) =>
% 121.77/16.29                                                     (((quantDeMorgan1) =>
% 121.77/16.29                                                       (((quantDeMorgan2) =>
% 121.77/16.29                                                         (((quantDeMorgan3) =>
% 121.77/16.29                                                           (((quantDeMorgan4) =>
% 121.77/16.29                                                             (((prop2setI) =>
% 121.77/16.29                                                               (((prop2set2propI) =>
% 121.77/16.29                                                                 (((notdexE) =>
% 121.77/16.29                                                                   (((notdallE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inCongP) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (in__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuE3u) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exu__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoin__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powerset__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunion__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (exuEu) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (descr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dsetconstr__Cong) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqimpsubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (emptysetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notsubsetI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (notequalI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetRefl) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTrans) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setadjoinSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subset2powerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetemptysetimpeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepInPowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (sepSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2IR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionEcases) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (disjointsetsI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectRsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (bs114d) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusERneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusELneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusILneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusIRneg) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusLsub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusSubset1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffI2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (symdiffIneg2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (secondinupair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairIR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairiskpair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowerset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletoninpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairset2E) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairsubunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairinpowunion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ubforcartprodlem3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempair) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionE2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setunionsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1I2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (singletonsuniq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theprop) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR11) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR12) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (upairequniteq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setukpairinjR) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ksndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (kpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndin) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemEL) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairmemER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodmempaircEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodfstpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodsndpairEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (cartprodpairsurjEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrSub) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrERa) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrEL2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (dpsetconstrER) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcImageSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (apProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (app) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (infuncsetfunc) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcinfuncset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamProp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lamp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2p) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (brelnall2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ex1E2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcextLem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcGraphProp4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (funcext2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ap2apEq2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (lam2lamEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (beta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eta2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalseProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueProp2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifSingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (ifp) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (theeq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrue) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iffalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (iftrueorfalse) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setminusT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementT_lem) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setextT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subsetTI) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (powersetTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTELcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binintersectTERcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contrasubsetT3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementI1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementE1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementSub2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (doubleComplementEq) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTnotintersectT) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementImpComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (contraSubsetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementTcontraSubset) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTILcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTIRcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTE) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (binunionTEcontra) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2a) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2b) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (demorgan2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule0) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz13rule4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_3) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_4) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (woz1_5) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all2) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1SetBreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (choice2fnsingleton) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1all1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (subbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (eqbreln1) =>
% 121.77/16.29                                                                     ((
% 121.77/16.29                                                                     (breln1invprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compEex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionCommutes) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2W) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2A) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2B) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Equiv) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncInj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (leftInvIsSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjCantorThm) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (foundation2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSclos) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peano0notS) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peanoSinj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ordinalMinLem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (!!) @ (
% 121.77/16.30                                                                     ^[Y0 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (ordinal @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y1 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y2 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y2 @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ 
% 121.77/16.30                                                                      Y2) =>
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.30      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl297])).
% 121.77/16.30  thf(zip_derived_cl312, plain,
% 121.77/16.30      (~ (((setadjoinE) =>
% 121.77/16.30           (((setadjoinOr) =>
% 121.77/16.30             (((setoftrueEq) =>
% 121.77/16.30               (((powersetI) =>
% 121.77/16.30                 (((emptyinPowerset) =>
% 121.77/16.30                   (((emptyInPowerset) =>
% 121.77/16.30                     (((powersetE) =>
% 121.77/16.30                       (((setunionI) =>
% 121.77/16.30                         (((setunionE) =>
% 121.77/16.30                           (((subPowSU) =>
% 121.77/16.30                             (((exuE2) =>
% 121.77/16.30                               (((nonemptyImpWitness) =>
% 121.77/16.30                                 (((uniqinunit) =>
% 121.77/16.30                                   (((notinsingleton) =>
% 121.77/16.30                                     (((eqinunit) =>
% 121.77/16.30                                       (((singletonsswitch) =>
% 121.77/16.30                                         (((upairsetE) =>
% 121.77/16.30                                           (((upairsetIL) =>
% 121.77/16.30                                             (((upairsetIR) =>
% 121.77/16.30                                               (((emptyE1) =>
% 121.77/16.30                                                 (((vacuousDall) =>
% 121.77/16.30                                                   (((quantDeMorgan1) =>
% 121.77/16.30                                                     (((quantDeMorgan2) =>
% 121.77/16.30                                                       (((quantDeMorgan3) =>
% 121.77/16.30                                                         (((quantDeMorgan4) =>
% 121.77/16.30                                                           (((prop2setI) =>
% 121.77/16.30                                                             (((prop2set2propI) =>
% 121.77/16.30                                                               (((notdexE) =>
% 121.77/16.30                                                                 (((notdallE) =>
% 121.77/16.30                                                                   (((exuI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuI3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inCongP) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (in__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuE3u) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exu__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoin__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powerset__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunion__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuEu) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (descr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dsetconstr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (emptysetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notsubsetI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetRefl) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTrans) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subset2powerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetemptysetimpeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepInPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2IR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (disjointsetsI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (bs114d) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusERneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusELneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusILneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusIRneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (secondinupair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairiskpair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairsubunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairinpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsuniq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR11) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR12) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairequniteq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempaircEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrERa) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcImageSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (apProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (app) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (infuncsetfunc) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcinfuncset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcextLem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2lamEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrue) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueorfalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTELcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTERcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTnotintersectT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementImpComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contraSubsetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTcontraSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTILcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTIRcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTEcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule0) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1all2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1SetBreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (choice2fnsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1all1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compEex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionCommutes) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2W) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2A) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2B) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Equiv) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncInj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (leftInvIsSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjCantorThm) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (foundation2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSclos) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peano0notS) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peanoSinj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ordinalMinLem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (!!) @ (
% 121.77/16.30                                                                     ^[Y0 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (ordinal @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y1 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y2 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y2 @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ 
% 121.77/16.30                                                                      Y2) =>
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.30      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl305])).
% 121.77/16.30  thf(zip_derived_cl318, plain,
% 121.77/16.30      (~ (((setadjoinOr) =>
% 121.77/16.30           (((setoftrueEq) =>
% 121.77/16.30             (((powersetI) =>
% 121.77/16.30               (((emptyinPowerset) =>
% 121.77/16.30                 (((emptyInPowerset) =>
% 121.77/16.30                   (((powersetE) =>
% 121.77/16.30                     (((setunionI) =>
% 121.77/16.30                       (((setunionE) =>
% 121.77/16.30                         (((subPowSU) =>
% 121.77/16.30                           (((exuE2) =>
% 121.77/16.30                             (((nonemptyImpWitness) =>
% 121.77/16.30                               (((uniqinunit) =>
% 121.77/16.30                                 (((notinsingleton) =>
% 121.77/16.30                                   (((eqinunit) =>
% 121.77/16.30                                     (((singletonsswitch) =>
% 121.77/16.30                                       (((upairsetE) =>
% 121.77/16.30                                         (((upairsetIL) =>
% 121.77/16.30                                           (((upairsetIR) =>
% 121.77/16.30                                             (((emptyE1) =>
% 121.77/16.30                                               (((vacuousDall) =>
% 121.77/16.30                                                 (((quantDeMorgan1) =>
% 121.77/16.30                                                   (((quantDeMorgan2) =>
% 121.77/16.30                                                     (((quantDeMorgan3) =>
% 121.77/16.30                                                       (((quantDeMorgan4) =>
% 121.77/16.30                                                         (((prop2setI) =>
% 121.77/16.30                                                           (((prop2set2propI) =>
% 121.77/16.30                                                             (((notdexE) =>
% 121.77/16.30                                                               (((notdallE) =>
% 121.77/16.30                                                                 (((exuI1) =>
% 121.77/16.30                                                                   (((exuI3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inCongP) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (in__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuE3u) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exu__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoin__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powerset__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunion__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuEu) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (descr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dsetconstr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (emptysetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notsubsetI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetRefl) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTrans) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subset2powerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetemptysetimpeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepInPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2IR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (disjointsetsI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (bs114d) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusERneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusELneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusILneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusIRneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (secondinupair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairiskpair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairsubunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairinpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsuniq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR11) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR12) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairequniteq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempaircEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrERa) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcImageSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (apProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (app) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (infuncsetfunc) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcinfuncset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcextLem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2lamEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrue) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueorfalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTELcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTERcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTnotintersectT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementImpComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contraSubsetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTcontraSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTILcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTIRcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTEcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule0) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1all2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1SetBreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (choice2fnsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1all1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compEex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionCommutes) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2W) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2A) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2B) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Equiv) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncInj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (leftInvIsSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjCantorThm) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (foundation2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSclos) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peano0notS) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peanoSinj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ordinalMinLem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (!!) @ (
% 121.77/16.30                                                                     ^[Y0 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (ordinal @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y1 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y2 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y2 @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ 
% 121.77/16.30                                                                      Y2) =>
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.30      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl312])).
% 121.77/16.30  thf(zip_derived_cl325, plain,
% 121.77/16.30      (~ (((setoftrueEq) =>
% 121.77/16.30           (((powersetI) =>
% 121.77/16.30             (((emptyinPowerset) =>
% 121.77/16.30               (((emptyInPowerset) =>
% 121.77/16.30                 (((powersetE) =>
% 121.77/16.30                   (((setunionI) =>
% 121.77/16.30                     (((setunionE) =>
% 121.77/16.30                       (((subPowSU) =>
% 121.77/16.30                         (((exuE2) =>
% 121.77/16.30                           (((nonemptyImpWitness) =>
% 121.77/16.30                             (((uniqinunit) =>
% 121.77/16.30                               (((notinsingleton) =>
% 121.77/16.30                                 (((eqinunit) =>
% 121.77/16.30                                   (((singletonsswitch) =>
% 121.77/16.30                                     (((upairsetE) =>
% 121.77/16.30                                       (((upairsetIL) =>
% 121.77/16.30                                         (((upairsetIR) =>
% 121.77/16.30                                           (((emptyE1) =>
% 121.77/16.30                                             (((vacuousDall) =>
% 121.77/16.30                                               (((quantDeMorgan1) =>
% 121.77/16.30                                                 (((quantDeMorgan2) =>
% 121.77/16.30                                                   (((quantDeMorgan3) =>
% 121.77/16.30                                                     (((quantDeMorgan4) =>
% 121.77/16.30                                                       (((prop2setI) =>
% 121.77/16.30                                                         (((prop2set2propI) =>
% 121.77/16.30                                                           (((notdexE) =>
% 121.77/16.30                                                             (((notdallE) =>
% 121.77/16.30                                                               (((exuI1) =>
% 121.77/16.30                                                                 (((exuI3) =>
% 121.77/16.30                                                                   (((exuI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inCongP) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (in__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuE3u) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exu__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoin__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powerset__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunion__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuEu) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (descr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dsetconstr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (emptysetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notsubsetI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetRefl) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTrans) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subset2powerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetemptysetimpeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepInPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2IR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (disjointsetsI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (bs114d) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusERneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusELneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusILneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusIRneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (secondinupair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairiskpair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairsubunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairinpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsuniq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR11) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR12) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairequniteq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempaircEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrERa) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcImageSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (apProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (app) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (infuncsetfunc) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcinfuncset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcextLem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2lamEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrue) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueorfalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTELcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTERcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTnotintersectT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementImpComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contraSubsetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTcontraSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTILcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTIRcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTEcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule0) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1all2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1SetBreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (choice2fnsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1all1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compEex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionCommutes) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2W) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2A) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2B) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Equiv) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncInj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (leftInvIsSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjCantorThm) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (foundation2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSclos) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peano0notS) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peanoSinj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ordinalMinLem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (!!) @ (
% 121.77/16.30                                                                     ^[Y0 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (ordinal @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y1 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y2 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y2 @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ 
% 121.77/16.30                                                                      Y2) =>
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.30      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl318])).
% 121.77/16.30  thf(zip_derived_cl331, plain,
% 121.77/16.30      (~ (((powersetI) =>
% 121.77/16.30           (((emptyinPowerset) =>
% 121.77/16.30             (((emptyInPowerset) =>
% 121.77/16.30               (((powersetE) =>
% 121.77/16.30                 (((setunionI) =>
% 121.77/16.30                   (((setunionE) =>
% 121.77/16.30                     (((subPowSU) =>
% 121.77/16.30                       (((exuE2) =>
% 121.77/16.30                         (((nonemptyImpWitness) =>
% 121.77/16.30                           (((uniqinunit) =>
% 121.77/16.30                             (((notinsingleton) =>
% 121.77/16.30                               (((eqinunit) =>
% 121.77/16.30                                 (((singletonsswitch) =>
% 121.77/16.30                                   (((upairsetE) =>
% 121.77/16.30                                     (((upairsetIL) =>
% 121.77/16.30                                       (((upairsetIR) =>
% 121.77/16.30                                         (((emptyE1) =>
% 121.77/16.30                                           (((vacuousDall) =>
% 121.77/16.30                                             (((quantDeMorgan1) =>
% 121.77/16.30                                               (((quantDeMorgan2) =>
% 121.77/16.30                                                 (((quantDeMorgan3) =>
% 121.77/16.30                                                   (((quantDeMorgan4) =>
% 121.77/16.30                                                     (((prop2setI) =>
% 121.77/16.30                                                       (((prop2set2propI) =>
% 121.77/16.30                                                         (((notdexE) =>
% 121.77/16.30                                                           (((notdallE) =>
% 121.77/16.30                                                             (((exuI1) =>
% 121.77/16.30                                                               (((exuI3) =>
% 121.77/16.30                                                                 (((exuI2) =>
% 121.77/16.30                                                                   (((inCongP) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (in__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuE3u) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exu__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoin__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powerset__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunion__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuEu) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (descr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dsetconstr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (emptysetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notsubsetI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetRefl) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTrans) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subset2powerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetemptysetimpeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepInPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2IR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (disjointsetsI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (bs114d) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusERneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusELneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusILneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusIRneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (secondinupair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairiskpair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairsubunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairinpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsuniq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR11) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR12) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairequniteq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempaircEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrERa) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcImageSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (apProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (app) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (infuncsetfunc) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcinfuncset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcextLem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2lamEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrue) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueorfalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTELcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTERcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTnotintersectT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementImpComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contraSubsetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTcontraSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTILcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTIRcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTEcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule0) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1all2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1SetBreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (choice2fnsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1all1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compEex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionCommutes) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2W) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2A) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2B) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Equiv) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncInj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (leftInvIsSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjCantorThm) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (foundation2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSclos) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peano0notS) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peanoSinj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ordinalMinLem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (!!) @ (
% 121.77/16.30                                                                     ^[Y0 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (ordinal @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y1 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y2 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y2 @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ 
% 121.77/16.30                                                                      Y2) =>
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.30      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl325])).
% 121.77/16.30  thf(zip_derived_cl337, plain,
% 121.77/16.30      (~ (((emptyinPowerset) =>
% 121.77/16.30           (((emptyInPowerset) =>
% 121.77/16.30             (((powersetE) =>
% 121.77/16.30               (((setunionI) =>
% 121.77/16.30                 (((setunionE) =>
% 121.77/16.30                   (((subPowSU) =>
% 121.77/16.30                     (((exuE2) =>
% 121.77/16.30                       (((nonemptyImpWitness) =>
% 121.77/16.30                         (((uniqinunit) =>
% 121.77/16.30                           (((notinsingleton) =>
% 121.77/16.30                             (((eqinunit) =>
% 121.77/16.30                               (((singletonsswitch) =>
% 121.77/16.30                                 (((upairsetE) =>
% 121.77/16.30                                   (((upairsetIL) =>
% 121.77/16.30                                     (((upairsetIR) =>
% 121.77/16.30                                       (((emptyE1) =>
% 121.77/16.30                                         (((vacuousDall) =>
% 121.77/16.30                                           (((quantDeMorgan1) =>
% 121.77/16.30                                             (((quantDeMorgan2) =>
% 121.77/16.30                                               (((quantDeMorgan3) =>
% 121.77/16.30                                                 (((quantDeMorgan4) =>
% 121.77/16.30                                                   (((prop2setI) =>
% 121.77/16.30                                                     (((prop2set2propI) =>
% 121.77/16.30                                                       (((notdexE) =>
% 121.77/16.30                                                         (((notdallE) =>
% 121.77/16.30                                                           (((exuI1) =>
% 121.77/16.30                                                             (((exuI3) =>
% 121.77/16.30                                                               (((exuI2) =>
% 121.77/16.30                                                                 (((inCongP) =>
% 121.77/16.30                                                                   (((in__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuE3u) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exu__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoin__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powerset__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunion__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuEu) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (descr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dsetconstr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (emptysetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notsubsetI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetRefl) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTrans) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subset2powerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetemptysetimpeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepInPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2IR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (disjointsetsI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (bs114d) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusERneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusELneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusILneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusIRneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (secondinupair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairiskpair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairsubunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairinpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsuniq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR11) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR12) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairequniteq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempaircEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrERa) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcImageSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (apProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (app) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (infuncsetfunc) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcinfuncset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcextLem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2lamEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrue) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueorfalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTELcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTERcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTnotintersectT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementImpComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contraSubsetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTcontraSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTILcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTIRcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTEcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule0) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1all2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1SetBreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (choice2fnsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1all1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compEex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionCommutes) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2W) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2A) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2B) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Equiv) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncInj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (leftInvIsSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjCantorThm) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (foundation2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSclos) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peano0notS) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peanoSinj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ordinalMinLem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (!!) @ (
% 121.77/16.30                                                                     ^[Y0 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (ordinal @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y1 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y2 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y2 @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ 
% 121.77/16.30                                                                      Y2) =>
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.30      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl331])).
% 121.77/16.30  thf(zip_derived_cl343, plain,
% 121.77/16.30      (~ (((emptyInPowerset) =>
% 121.77/16.30           (((powersetE) =>
% 121.77/16.30             (((setunionI) =>
% 121.77/16.30               (((setunionE) =>
% 121.77/16.30                 (((subPowSU) =>
% 121.77/16.30                   (((exuE2) =>
% 121.77/16.30                     (((nonemptyImpWitness) =>
% 121.77/16.30                       (((uniqinunit) =>
% 121.77/16.30                         (((notinsingleton) =>
% 121.77/16.30                           (((eqinunit) =>
% 121.77/16.30                             (((singletonsswitch) =>
% 121.77/16.30                               (((upairsetE) =>
% 121.77/16.30                                 (((upairsetIL) =>
% 121.77/16.30                                   (((upairsetIR) =>
% 121.77/16.30                                     (((emptyE1) =>
% 121.77/16.30                                       (((vacuousDall) =>
% 121.77/16.30                                         (((quantDeMorgan1) =>
% 121.77/16.30                                           (((quantDeMorgan2) =>
% 121.77/16.30                                             (((quantDeMorgan3) =>
% 121.77/16.30                                               (((quantDeMorgan4) =>
% 121.77/16.30                                                 (((prop2setI) =>
% 121.77/16.30                                                   (((prop2set2propI) =>
% 121.77/16.30                                                     (((notdexE) =>
% 121.77/16.30                                                       (((notdallE) =>
% 121.77/16.30                                                         (((exuI1) =>
% 121.77/16.30                                                           (((exuI3) =>
% 121.77/16.30                                                             (((exuI2) =>
% 121.77/16.30                                                               (((inCongP) =>
% 121.77/16.30                                                                 (((in__Cong) =>
% 121.77/16.30                                                                   (((exuE3u) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exu__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoin__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powerset__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunion__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuEu) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (descr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dsetconstr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (emptysetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notsubsetI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetRefl) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTrans) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subset2powerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetemptysetimpeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepInPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2IR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (disjointsetsI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (bs114d) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusERneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusELneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusILneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusIRneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (secondinupair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairiskpair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairsubunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairinpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsuniq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR11) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR12) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairequniteq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempaircEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrERa) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcImageSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (apProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (app) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (infuncsetfunc) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcinfuncset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcextLem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2lamEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrue) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueorfalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTELcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTERcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTnotintersectT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementImpComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contraSubsetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTcontraSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTILcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTIRcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTEcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule0) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1all2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1SetBreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (choice2fnsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1all1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1invE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1compEex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (breln1unionCommutes) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2W) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2A) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz2B) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Ex1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1Equiv) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (image1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncInInjFuncSet) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (injFuncSetFuncInj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncIn) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjFuncSetFuncSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (leftInvIsSurj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (surjCantorThm) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (foundation2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notinself2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (omegaSclos) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peano0notS) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (peanoSinj) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (transitivesetOp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionTransitive) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ordinalMinLem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (!!) @ (
% 121.77/16.30                                                                     ^[Y0 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (ordinal @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y1 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (!!) @ (
% 121.77/16.30                                                                      ^[Y2 : $i]:
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y2 @ 
% 121.77/16.30                                                                      Y0) =>
% 121.77/16.30                                                                      ((
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ 
% 121.77/16.30                                                                      Y2) =>
% 121.77/16.30                                                                      (in @ 
% 121.77/16.30                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 121.77/16.30      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl337])).
% 121.77/16.30  thf(zip_derived_cl350, plain,
% 121.77/16.30      (~ (((powersetE) =>
% 121.77/16.30           (((setunionI) =>
% 121.77/16.30             (((setunionE) =>
% 121.77/16.30               (((subPowSU) =>
% 121.77/16.30                 (((exuE2) =>
% 121.77/16.30                   (((nonemptyImpWitness) =>
% 121.77/16.30                     (((uniqinunit) =>
% 121.77/16.30                       (((notinsingleton) =>
% 121.77/16.30                         (((eqinunit) =>
% 121.77/16.30                           (((singletonsswitch) =>
% 121.77/16.30                             (((upairsetE) =>
% 121.77/16.30                               (((upairsetIL) =>
% 121.77/16.30                                 (((upairsetIR) =>
% 121.77/16.30                                   (((emptyE1) =>
% 121.77/16.30                                     (((vacuousDall) =>
% 121.77/16.30                                       (((quantDeMorgan1) =>
% 121.77/16.30                                         (((quantDeMorgan2) =>
% 121.77/16.30                                           (((quantDeMorgan3) =>
% 121.77/16.30                                             (((quantDeMorgan4) =>
% 121.77/16.30                                               (((prop2setI) =>
% 121.77/16.30                                                 (((prop2set2propI) =>
% 121.77/16.30                                                   (((notdexE) =>
% 121.77/16.30                                                     (((notdallE) =>
% 121.77/16.30                                                       (((exuI1) =>
% 121.77/16.30                                                         (((exuI3) =>
% 121.77/16.30                                                           (((exuI2) =>
% 121.77/16.30                                                             (((inCongP) =>
% 121.77/16.30                                                               (((in__Cong) =>
% 121.77/16.30                                                                 (((exuE3u) =>
% 121.77/16.30                                                                   (((exu__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoin__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powerset__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunion__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (exuEu) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (descr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dsetconstr__Cong) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqimpsubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (emptysetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notsubsetI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (notequalI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetRefl) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTrans) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setadjoinSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subset2powerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetemptysetimpeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepInPowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (sepSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2IR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionEcases) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset5) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (disjointsetsI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectRsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (bs114d) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusERneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusELneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusILneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusIRneg) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusLsub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusSubset1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffI2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (symdiffIneg2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (secondinupair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairIR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairiskpair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowerset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletoninpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairset2E) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairsubunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairinpowunion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ubforcartprodlem3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempair) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionE2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setunionsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1I2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (singletonsuniq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theprop) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR11) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR12) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (upairequniteq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setukpairinjR) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndsingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ksndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (kpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndin) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemEL) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairmemER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodmempaircEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodfstpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodsndpairEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (cartprodpairsurjEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrSub) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setOfPairsIsBReln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrERa) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrEL2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (dpsetconstrER) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcImageSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (apProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (app) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (infuncsetfunc) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcinfuncset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamProp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lamp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2p) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (brelnall2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ex1E2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcextLem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcGraphProp4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eqbreln) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (funcext2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ap2apEq2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (lam2lamEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (beta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (eta2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalseProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueProp2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifSingleton) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (ifp) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (theeq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrue) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iffalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (iftrueorfalse) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setminusT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementT_lem) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (setextT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (subsetTI) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (powersetTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTELcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binintersectTERcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contrasubsetT3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementI1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementE1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementSub2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (doubleComplementEq) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTnotintersectT) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementImpComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementSubsetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementInPowersetComplementIntersect) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (contraSubsetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementTcontraSubset) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTILcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTIRcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInUnion2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inIntersectImpInIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (intersectInPowersetIntersectUnions) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpNotIn1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (inComplementUnionImpInComplement1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTE) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (binunionTEcontra) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (complementUnionInPowersetComplement) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2a) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2b) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (demorgan2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule0) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule3) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz13rule4) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_1) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_2) =>
% 121.77/16.30                                                                     ((
% 121.77/16.30                                                                     (woz1_3) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz1_4) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz1_5) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1all2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1SetBreln1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (choice2fnsingleton) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1all1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subbreln1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (eqbreln1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1invprop) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1invI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1invE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1compprop) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1compI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1compE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1compEex) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionprop) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionIL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionIR) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionEcases) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionCommutes) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz2Ex) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz2W) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz2A) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz2B) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (image1Ex) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (image1Ex1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (image1Equiv) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (image1E) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (image1I) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (injFuncSetFuncIn) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (injFuncSetFuncInj) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (leftInvIsSurj) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (surjCantorThm) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (foundation2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (notinself) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (notinself2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (omegaSp) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (omegaSclos) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (peano0notS) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (peanoSinj) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (transitivesetOp1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintTransitive) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (transitivesetOp2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setunionTransitive) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ordinalMinLem1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (!!) @ (
% 122.15/16.30                                                                     ^[Y0 : $i]:
% 122.15/16.30                                                                      ((
% 122.15/16.30                                                                      (ordinal @ 
% 122.15/16.30                                                                      Y0) =>
% 122.15/16.30                                                                      ((
% 122.15/16.30                                                                      (!!) @ (
% 122.15/16.30                                                                      ^[Y1 : $i]:
% 122.15/16.30                                                                      ((
% 122.15/16.30                                                                      (!!) @ (
% 122.15/16.30                                                                      ^[Y2 : $i]:
% 122.15/16.30                                                                      ((
% 122.15/16.30                                                                      (in @ 
% 122.15/16.30                                                                      Y2 @ 
% 122.15/16.30                                                                      Y0) =>
% 122.15/16.30                                                                      ((
% 122.15/16.30                                                                      (in @ 
% 122.15/16.30                                                                      Y1 @ 
% 122.15/16.30                                                                      Y2) =>
% 122.15/16.30                                                                      (in @ 
% 122.15/16.30                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.30      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl343])).
% 122.15/16.30  thf(zip_derived_cl357, plain,
% 122.15/16.30      (~ (((setunionI) =>
% 122.15/16.30           (((setunionE) =>
% 122.15/16.30             (((subPowSU) =>
% 122.15/16.30               (((exuE2) =>
% 122.15/16.30                 (((nonemptyImpWitness) =>
% 122.15/16.30                   (((uniqinunit) =>
% 122.15/16.30                     (((notinsingleton) =>
% 122.15/16.30                       (((eqinunit) =>
% 122.15/16.30                         (((singletonsswitch) =>
% 122.15/16.30                           (((upairsetE) =>
% 122.15/16.30                             (((upairsetIL) =>
% 122.15/16.30                               (((upairsetIR) =>
% 122.15/16.30                                 (((emptyE1) =>
% 122.15/16.30                                   (((vacuousDall) =>
% 122.15/16.30                                     (((quantDeMorgan1) =>
% 122.15/16.30                                       (((quantDeMorgan2) =>
% 122.15/16.30                                         (((quantDeMorgan3) =>
% 122.15/16.30                                           (((quantDeMorgan4) =>
% 122.15/16.30                                             (((prop2setI) =>
% 122.15/16.30                                               (((prop2set2propI) =>
% 122.15/16.30                                                 (((notdexE) =>
% 122.15/16.30                                                   (((notdallE) =>
% 122.15/16.30                                                     (((exuI1) =>
% 122.15/16.30                                                       (((exuI3) =>
% 122.15/16.30                                                         (((exuI2) =>
% 122.15/16.30                                                           (((inCongP) =>
% 122.15/16.30                                                             (((in__Cong) =>
% 122.15/16.30                                                               (((exuE3u) =>
% 122.15/16.30                                                                 (((exu__Cong) =>
% 122.15/16.30                                                                   (((setadjoin__Cong) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (powerset__Cong) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setunion__Cong) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (exuEu) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (descr__Cong) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (dsetconstr__Cong) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (eqimpsubset2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (eqimpsubset1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetI2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (emptysetsubset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetE2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (notsubsetI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (notequalI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (notequalI2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetRefl) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetTrans) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setadjoinSub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setadjoinSub2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subset2powerset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setextsub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetemptysetimpeq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (powersetI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (powersetE1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (inPowerset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (powersetsubset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (sepInPowerset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (sepSubset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionIL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (upairset2IR) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionIR) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionEcases) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionLsub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionRsub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectSubset5) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectEL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectLsub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectSubset2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectSubset3) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectER) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (disjointsetsI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectRsub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectSubset4) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectSubset1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (bs114d) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusEL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusER) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusSubset2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusERneg) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusELneg) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusILneg) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusIRneg) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusLsub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusSubset1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (symdiffE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (symdiffI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (symdiffI2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (symdiffIneg1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (symdiffIneg2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (secondinupair) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairIL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairIR) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (kpairiskpair) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (kpairp) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (singletonsubset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (singletoninpowerset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (singletoninpowunion) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (upairset2E) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (upairsubunion) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (upairinpowunion) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ubforcartprodlem1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ubforcartprodlem2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ubforcartprodlem3) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodpairin) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodmempair1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodmempair) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setunionE2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setunionsingleton1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setunionsingleton2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setunionsingleton) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (singletonprop) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ex1E1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ex1I) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ex1I2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (singletonsuniq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairinjL1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (kfstsingleton) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (theprop) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (kfstpairEq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodfstin) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairinjL2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairinjL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairinjR11) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairinjR12) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairinjR1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (upairequniteq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairinjR2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairinjR) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ksndsingleton) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ksndpairEq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (kpairsurjEq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodsndin) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodpairmemEL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodpairmemER) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodmempaircEq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodfstpairEq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodsndpairEq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodpairsurjEq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (dpsetconstrI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (dpsetconstrSub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setOfPairsIsBReln) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (dpsetconstrERa) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (dpsetconstrEL1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (dpsetconstrEL2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (dpsetconstrER) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (funcImageSingleton) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (apProp) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (app) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (infuncsetfunc) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ap2p) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (funcinfuncset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (lamProp) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (lamp) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (lam2p) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (brelnall1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (brelnall2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ex1E2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (funcGraphProp1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (funcGraphProp3) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (funcGraphProp2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (funcextLem) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (funcGraphProp4) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subbreln) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (eqbreln) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (funcext) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (funcext2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ap2apEq1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ap2apEq2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (beta1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (eta1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (lam2lamEq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (beta2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (eta2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (iffalseProp1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (iffalseProp2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (iftrueProp1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (iftrueProp2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ifSingleton) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ifp) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (theeq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (iftrue) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (iffalse) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (iftrueorfalse) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectT_lem) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionT_lem) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (powersetT_lem) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusT_lem) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (complementT_lem) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setextT) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetTI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (powersetTI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (powersetTE1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (complementTI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (complementTE1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectTELcontra) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectTERcontra) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (contrasubsetT) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (contrasubsetT1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (contrasubsetT2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (contrasubsetT3) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (doubleComplementI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (doubleComplementE1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (doubleComplementSub1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (doubleComplementSub2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (doubleComplementEq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (complementTnotintersectT) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (complementImpComplementIntersect) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (contraSubsetComplement) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (complementTcontraSubset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionTILcontra) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionTIRcontra) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (inIntersectImpInUnion) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionTE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionTEcontra) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (demorgan2a1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (demorgan2a2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (demorgan1a) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (demorgan1b) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (demorgan1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (demorgan2a) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (demorgan2b2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (demorgan2b) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (demorgan2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz13rule0) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz13rule1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz13rule2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz13rule3) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz13rule4) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz1_1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz1_2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz1_3) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz1_4) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz1_5) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1all2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1SetBreln1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (choice2fnsingleton) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1all1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subbreln1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (eqbreln1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1invprop) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1invI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1invE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1compprop) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1compI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1compE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1compEex) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionprop) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionIL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionIR) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionEcases) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (breln1unionCommutes) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz2Ex) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz2W) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz2A) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (woz2B) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (image1Ex) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (image1Ex1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (image1Equiv) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (image1E) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (image1I) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (injFuncSetFuncIn) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (injFuncSetFuncInj) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (leftInvIsSurj) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (surjCantorThm) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (foundation2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (notinself) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (notinself2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (omegaSp) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (omegaSclos) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (peano0notS) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (peanoSinj) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (transitivesetOp1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintTransitive) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (transitivesetOp2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setunionTransitive) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ordinalMinLem1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (!!) @ (
% 122.15/16.30                                                                     ^[Y0 : $i]:
% 122.15/16.30                                                                      ((
% 122.15/16.30                                                                      (ordinal @ 
% 122.15/16.30                                                                      Y0) =>
% 122.15/16.30                                                                      ((
% 122.15/16.30                                                                      (!!) @ (
% 122.15/16.30                                                                      ^[Y1 : $i]:
% 122.15/16.30                                                                      ((
% 122.15/16.30                                                                      (!!) @ (
% 122.15/16.30                                                                      ^[Y2 : $i]:
% 122.15/16.30                                                                      ((
% 122.15/16.30                                                                      (in @ 
% 122.15/16.30                                                                      Y2 @ 
% 122.15/16.30                                                                      Y0) =>
% 122.15/16.30                                                                      ((
% 122.15/16.30                                                                      (in @ 
% 122.15/16.30                                                                      Y1 @ 
% 122.15/16.30                                                                      Y2) =>
% 122.15/16.30                                                                      (in @ 
% 122.15/16.30                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.30      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl350])).
% 122.15/16.30  thf(zip_derived_cl364, plain,
% 122.15/16.30      (~ (((setunionE) =>
% 122.15/16.30           (((subPowSU) =>
% 122.15/16.30             (((exuE2) =>
% 122.15/16.30               (((nonemptyImpWitness) =>
% 122.15/16.30                 (((uniqinunit) =>
% 122.15/16.30                   (((notinsingleton) =>
% 122.15/16.30                     (((eqinunit) =>
% 122.15/16.30                       (((singletonsswitch) =>
% 122.15/16.30                         (((upairsetE) =>
% 122.15/16.30                           (((upairsetIL) =>
% 122.15/16.30                             (((upairsetIR) =>
% 122.15/16.30                               (((emptyE1) =>
% 122.15/16.30                                 (((vacuousDall) =>
% 122.15/16.30                                   (((quantDeMorgan1) =>
% 122.15/16.30                                     (((quantDeMorgan2) =>
% 122.15/16.30                                       (((quantDeMorgan3) =>
% 122.15/16.30                                         (((quantDeMorgan4) =>
% 122.15/16.30                                           (((prop2setI) =>
% 122.15/16.30                                             (((prop2set2propI) =>
% 122.15/16.30                                               (((notdexE) =>
% 122.15/16.30                                                 (((notdallE) =>
% 122.15/16.30                                                   (((exuI1) =>
% 122.15/16.30                                                     (((exuI3) =>
% 122.15/16.30                                                       (((exuI2) =>
% 122.15/16.30                                                         (((inCongP) =>
% 122.15/16.30                                                           (((in__Cong) =>
% 122.15/16.30                                                             (((exuE3u) =>
% 122.15/16.30                                                               (((exu__Cong) =>
% 122.15/16.30                                                                 (((setadjoin__Cong) =>
% 122.15/16.30                                                                   (((powerset__Cong) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setunion__Cong) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (exuEu) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (descr__Cong) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (dsetconstr__Cong) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (eqimpsubset2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (eqimpsubset1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetI2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (emptysetsubset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetE2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (notsubsetI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (notequalI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (notequalI2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetRefl) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetTrans) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setadjoinSub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setadjoinSub2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subset2powerset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setextsub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (subsetemptysetimpeq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (powersetI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (powersetE1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (inPowerset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (powersetsubset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (sepInPowerset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (sepSubset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionIL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (upairset2IR) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionIR) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionEcases) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionLsub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binunionRsub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectSubset5) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectEL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectLsub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectSubset2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectSubset3) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectER) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (disjointsetsI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectRsub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectSubset4) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (binintersectSubset1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (bs114d) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusI) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusEL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusER) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusSubset2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusERneg) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusELneg) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusILneg) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusIRneg) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusLsub) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setminusSubset1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (symdiffE) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (symdiffI1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (symdiffI2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (symdiffIneg1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (symdiffIneg2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (secondinupair) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairIL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairIR) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (kpairiskpair) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (kpairp) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (singletonsubset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (singletoninpowerset) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (singletoninpowunion) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (upairset2E) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (upairsubunion) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (upairinpowunion) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ubforcartprodlem1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ubforcartprodlem2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ubforcartprodlem3) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodpairin) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodmempair1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodmempair) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setunionE2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setunionsingleton1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setunionsingleton2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setunionsingleton) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (singletonprop) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ex1E1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ex1I) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (ex1I2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (singletonsuniq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairinjL1) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (kfstsingleton) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (theprop) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (kfstpairEq) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (cartprodfstin) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairinjL2) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairinjL) =>
% 122.15/16.30                                                                     ((
% 122.15/16.30                                                                     (setukpairinjR11) =>
% 122.15/16.30                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR12) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairequniteq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempaircEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrERa) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcImageSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (apProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (app) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (infuncsetfunc) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcinfuncset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcextLem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2lamEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrue) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueorfalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTELcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTERcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTnotintersectT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementImpComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contraSubsetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTcontraSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTILcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTIRcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTEcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule0) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1SetBreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (choice2fnsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compEex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionCommutes) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2W) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2A) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2B) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Equiv) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncInj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (leftInvIsSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjCantorThm) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (foundation2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSclos) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peano0notS) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peanoSinj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ordinalMinLem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (!!) @ (
% 122.15/16.31                                                                     ^[Y0 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (ordinal @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y1 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y2 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y2 @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ 
% 122.15/16.31                                                                      Y2) =>
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.31      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl357])).
% 122.15/16.31  thf(zip_derived_cl372, plain,
% 122.15/16.31      (~ (((subPowSU) =>
% 122.15/16.31           (((exuE2) =>
% 122.15/16.31             (((nonemptyImpWitness) =>
% 122.15/16.31               (((uniqinunit) =>
% 122.15/16.31                 (((notinsingleton) =>
% 122.15/16.31                   (((eqinunit) =>
% 122.15/16.31                     (((singletonsswitch) =>
% 122.15/16.31                       (((upairsetE) =>
% 122.15/16.31                         (((upairsetIL) =>
% 122.15/16.31                           (((upairsetIR) =>
% 122.15/16.31                             (((emptyE1) =>
% 122.15/16.31                               (((vacuousDall) =>
% 122.15/16.31                                 (((quantDeMorgan1) =>
% 122.15/16.31                                   (((quantDeMorgan2) =>
% 122.15/16.31                                     (((quantDeMorgan3) =>
% 122.15/16.31                                       (((quantDeMorgan4) =>
% 122.15/16.31                                         (((prop2setI) =>
% 122.15/16.31                                           (((prop2set2propI) =>
% 122.15/16.31                                             (((notdexE) =>
% 122.15/16.31                                               (((notdallE) =>
% 122.15/16.31                                                 (((exuI1) =>
% 122.15/16.31                                                   (((exuI3) =>
% 122.15/16.31                                                     (((exuI2) =>
% 122.15/16.31                                                       (((inCongP) =>
% 122.15/16.31                                                         (((in__Cong) =>
% 122.15/16.31                                                           (((exuE3u) =>
% 122.15/16.31                                                             (((exu__Cong) =>
% 122.15/16.31                                                               (((setadjoin__Cong) =>
% 122.15/16.31                                                                 (((powerset__Cong) =>
% 122.15/16.31                                                                   (((setunion__Cong) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (exuEu) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (descr__Cong) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dsetconstr__Cong) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqimpsubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqimpsubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (emptysetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notsubsetI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetRefl) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTrans) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subset2powerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetemptysetimpeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepInPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2IR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (disjointsetsI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (bs114d) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusERneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusELneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusILneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusIRneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (secondinupair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairiskpair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairsubunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairinpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsuniq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR11) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR12) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairequniteq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempaircEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrERa) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcImageSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (apProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (app) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (infuncsetfunc) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcinfuncset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcextLem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2lamEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrue) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueorfalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTELcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTERcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTnotintersectT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementImpComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contraSubsetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTcontraSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTILcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTIRcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTEcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule0) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1SetBreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (choice2fnsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compEex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionCommutes) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2W) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2A) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2B) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Equiv) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncInj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (leftInvIsSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjCantorThm) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (foundation2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSclos) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peano0notS) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peanoSinj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ordinalMinLem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (!!) @ (
% 122.15/16.31                                                                     ^[Y0 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (ordinal @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y1 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y2 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y2 @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ 
% 122.15/16.31                                                                      Y2) =>
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.31      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl364])).
% 122.15/16.31  thf(zip_derived_cl382, plain,
% 122.15/16.31      (~ (((exuE2) =>
% 122.15/16.31           (((nonemptyImpWitness) =>
% 122.15/16.31             (((uniqinunit) =>
% 122.15/16.31               (((notinsingleton) =>
% 122.15/16.31                 (((eqinunit) =>
% 122.15/16.31                   (((singletonsswitch) =>
% 122.15/16.31                     (((upairsetE) =>
% 122.15/16.31                       (((upairsetIL) =>
% 122.15/16.31                         (((upairsetIR) =>
% 122.15/16.31                           (((emptyE1) =>
% 122.15/16.31                             (((vacuousDall) =>
% 122.15/16.31                               (((quantDeMorgan1) =>
% 122.15/16.31                                 (((quantDeMorgan2) =>
% 122.15/16.31                                   (((quantDeMorgan3) =>
% 122.15/16.31                                     (((quantDeMorgan4) =>
% 122.15/16.31                                       (((prop2setI) =>
% 122.15/16.31                                         (((prop2set2propI) =>
% 122.15/16.31                                           (((notdexE) =>
% 122.15/16.31                                             (((notdallE) =>
% 122.15/16.31                                               (((exuI1) =>
% 122.15/16.31                                                 (((exuI3) =>
% 122.15/16.31                                                   (((exuI2) =>
% 122.15/16.31                                                     (((inCongP) =>
% 122.15/16.31                                                       (((in__Cong) =>
% 122.15/16.31                                                         (((exuE3u) =>
% 122.15/16.31                                                           (((exu__Cong) =>
% 122.15/16.31                                                             (((setadjoin__Cong) =>
% 122.15/16.31                                                               (((powerset__Cong) =>
% 122.15/16.31                                                                 (((setunion__Cong) =>
% 122.15/16.31                                                                   (((exuEu) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (descr__Cong) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dsetconstr__Cong) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqimpsubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqimpsubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (emptysetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notsubsetI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetRefl) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTrans) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subset2powerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetemptysetimpeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepInPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2IR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (disjointsetsI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (bs114d) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusERneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusELneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusILneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusIRneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (secondinupair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairiskpair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairsubunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairinpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsuniq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR11) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR12) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairequniteq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempaircEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrERa) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcImageSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (apProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (app) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (infuncsetfunc) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcinfuncset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcextLem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2lamEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrue) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueorfalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTELcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTERcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTnotintersectT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementImpComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contraSubsetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTcontraSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTILcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTIRcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTEcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule0) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1SetBreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (choice2fnsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compEex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionCommutes) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2W) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2A) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2B) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Equiv) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncInj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (leftInvIsSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjCantorThm) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (foundation2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSclos) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peano0notS) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peanoSinj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ordinalMinLem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (!!) @ (
% 122.15/16.31                                                                     ^[Y0 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (ordinal @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y1 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y2 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y2 @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ 
% 122.15/16.31                                                                      Y2) =>
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.31      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl372])).
% 122.15/16.31  thf(zip_derived_cl390, plain,
% 122.15/16.31      (~ (((nonemptyImpWitness) =>
% 122.15/16.31           (((uniqinunit) =>
% 122.15/16.31             (((notinsingleton) =>
% 122.15/16.31               (((eqinunit) =>
% 122.15/16.31                 (((singletonsswitch) =>
% 122.15/16.31                   (((upairsetE) =>
% 122.15/16.31                     (((upairsetIL) =>
% 122.15/16.31                       (((upairsetIR) =>
% 122.15/16.31                         (((emptyE1) =>
% 122.15/16.31                           (((vacuousDall) =>
% 122.15/16.31                             (((quantDeMorgan1) =>
% 122.15/16.31                               (((quantDeMorgan2) =>
% 122.15/16.31                                 (((quantDeMorgan3) =>
% 122.15/16.31                                   (((quantDeMorgan4) =>
% 122.15/16.31                                     (((prop2setI) =>
% 122.15/16.31                                       (((prop2set2propI) =>
% 122.15/16.31                                         (((notdexE) =>
% 122.15/16.31                                           (((notdallE) =>
% 122.15/16.31                                             (((exuI1) =>
% 122.15/16.31                                               (((exuI3) =>
% 122.15/16.31                                                 (((exuI2) =>
% 122.15/16.31                                                   (((inCongP) =>
% 122.15/16.31                                                     (((in__Cong) =>
% 122.15/16.31                                                       (((exuE3u) =>
% 122.15/16.31                                                         (((exu__Cong) =>
% 122.15/16.31                                                           (((setadjoin__Cong) =>
% 122.15/16.31                                                             (((powerset__Cong) =>
% 122.15/16.31                                                               (((setunion__Cong) =>
% 122.15/16.31                                                                 (((exuEu) =>
% 122.15/16.31                                                                   (((descr__Cong) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dsetconstr__Cong) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqimpsubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqimpsubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (emptysetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notsubsetI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetRefl) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTrans) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subset2powerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetemptysetimpeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepInPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2IR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (disjointsetsI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (bs114d) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusERneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusELneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusILneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusIRneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (secondinupair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairiskpair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairsubunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairinpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsuniq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR11) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR12) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairequniteq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempaircEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrERa) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcImageSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (apProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (app) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (infuncsetfunc) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcinfuncset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcextLem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2lamEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrue) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueorfalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTELcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTERcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTnotintersectT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementImpComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contraSubsetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTcontraSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTILcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTIRcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTEcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule0) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1SetBreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (choice2fnsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compEex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionCommutes) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2W) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2A) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2B) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Equiv) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncInj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (leftInvIsSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjCantorThm) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (foundation2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSclos) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peano0notS) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peanoSinj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ordinalMinLem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (!!) @ (
% 122.15/16.31                                                                     ^[Y0 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (ordinal @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y1 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y2 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y2 @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ 
% 122.15/16.31                                                                      Y2) =>
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.31      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl382])).
% 122.15/16.31  thf(zip_derived_cl397, plain,
% 122.15/16.31      (~ (((uniqinunit) =>
% 122.15/16.31           (((notinsingleton) =>
% 122.15/16.31             (((eqinunit) =>
% 122.15/16.31               (((singletonsswitch) =>
% 122.15/16.31                 (((upairsetE) =>
% 122.15/16.31                   (((upairsetIL) =>
% 122.15/16.31                     (((upairsetIR) =>
% 122.15/16.31                       (((emptyE1) =>
% 122.15/16.31                         (((vacuousDall) =>
% 122.15/16.31                           (((quantDeMorgan1) =>
% 122.15/16.31                             (((quantDeMorgan2) =>
% 122.15/16.31                               (((quantDeMorgan3) =>
% 122.15/16.31                                 (((quantDeMorgan4) =>
% 122.15/16.31                                   (((prop2setI) =>
% 122.15/16.31                                     (((prop2set2propI) =>
% 122.15/16.31                                       (((notdexE) =>
% 122.15/16.31                                         (((notdallE) =>
% 122.15/16.31                                           (((exuI1) =>
% 122.15/16.31                                             (((exuI3) =>
% 122.15/16.31                                               (((exuI2) =>
% 122.15/16.31                                                 (((inCongP) =>
% 122.15/16.31                                                   (((in__Cong) =>
% 122.15/16.31                                                     (((exuE3u) =>
% 122.15/16.31                                                       (((exu__Cong) =>
% 122.15/16.31                                                         (((setadjoin__Cong) =>
% 122.15/16.31                                                           (((powerset__Cong) =>
% 122.15/16.31                                                             (((setunion__Cong) =>
% 122.15/16.31                                                               (((exuEu) =>
% 122.15/16.31                                                                 (((descr__Cong) =>
% 122.15/16.31                                                                   (((dsetconstr__Cong) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqimpsubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqimpsubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (emptysetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notsubsetI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetRefl) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTrans) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subset2powerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetemptysetimpeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepInPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2IR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (disjointsetsI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (bs114d) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusERneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusELneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusILneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusIRneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (secondinupair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairiskpair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairsubunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairinpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsuniq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR11) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR12) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairequniteq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempaircEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrERa) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcImageSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (apProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (app) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (infuncsetfunc) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcinfuncset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcextLem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2lamEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrue) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueorfalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTELcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTERcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTnotintersectT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementImpComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contraSubsetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTcontraSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTILcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTIRcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTEcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule0) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1SetBreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (choice2fnsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compEex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionCommutes) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2W) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2A) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2B) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Equiv) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncInj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (leftInvIsSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjCantorThm) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (foundation2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSclos) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peano0notS) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peanoSinj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ordinalMinLem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (!!) @ (
% 122.15/16.31                                                                     ^[Y0 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (ordinal @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y1 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y2 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y2 @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ 
% 122.15/16.31                                                                      Y2) =>
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.31      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl390])).
% 122.15/16.31  thf(zip_derived_cl406, plain,
% 122.15/16.31      (~ (((notinsingleton) =>
% 122.15/16.31           (((eqinunit) =>
% 122.15/16.31             (((singletonsswitch) =>
% 122.15/16.31               (((upairsetE) =>
% 122.15/16.31                 (((upairsetIL) =>
% 122.15/16.31                   (((upairsetIR) =>
% 122.15/16.31                     (((emptyE1) =>
% 122.15/16.31                       (((vacuousDall) =>
% 122.15/16.31                         (((quantDeMorgan1) =>
% 122.15/16.31                           (((quantDeMorgan2) =>
% 122.15/16.31                             (((quantDeMorgan3) =>
% 122.15/16.31                               (((quantDeMorgan4) =>
% 122.15/16.31                                 (((prop2setI) =>
% 122.15/16.31                                   (((prop2set2propI) =>
% 122.15/16.31                                     (((notdexE) =>
% 122.15/16.31                                       (((notdallE) =>
% 122.15/16.31                                         (((exuI1) =>
% 122.15/16.31                                           (((exuI3) =>
% 122.15/16.31                                             (((exuI2) =>
% 122.15/16.31                                               (((inCongP) =>
% 122.15/16.31                                                 (((in__Cong) =>
% 122.15/16.31                                                   (((exuE3u) =>
% 122.15/16.31                                                     (((exu__Cong) =>
% 122.15/16.31                                                       (((setadjoin__Cong) =>
% 122.15/16.31                                                         (((powerset__Cong) =>
% 122.15/16.31                                                           (((setunion__Cong) =>
% 122.15/16.31                                                             (((exuEu) =>
% 122.15/16.31                                                               (((descr__Cong) =>
% 122.15/16.31                                                                 (((dsetconstr__Cong) =>
% 122.15/16.31                                                                   (((subsetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqimpsubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqimpsubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (emptysetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notsubsetI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetRefl) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTrans) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subset2powerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetemptysetimpeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepInPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2IR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (disjointsetsI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (bs114d) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusERneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusELneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusILneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusIRneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (secondinupair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairiskpair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairsubunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairinpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsuniq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR11) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR12) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairequniteq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempaircEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrERa) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcImageSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (apProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (app) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (infuncsetfunc) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcinfuncset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcextLem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2lamEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrue) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueorfalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTELcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTERcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTnotintersectT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementImpComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contraSubsetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTcontraSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTILcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTIRcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTEcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule0) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1SetBreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (choice2fnsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compEex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionCommutes) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2W) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2A) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2B) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Equiv) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncInj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (leftInvIsSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjCantorThm) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (foundation2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSclos) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peano0notS) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peanoSinj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ordinalMinLem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (!!) @ (
% 122.15/16.31                                                                     ^[Y0 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (ordinal @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y1 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y2 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y2 @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ 
% 122.15/16.31                                                                      Y2) =>
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.31      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl397])).
% 122.15/16.31  thf(zip_derived_cl413, plain,
% 122.15/16.31      (~ (((eqinunit) =>
% 122.15/16.31           (((singletonsswitch) =>
% 122.15/16.31             (((upairsetE) =>
% 122.15/16.31               (((upairsetIL) =>
% 122.15/16.31                 (((upairsetIR) =>
% 122.15/16.31                   (((emptyE1) =>
% 122.15/16.31                     (((vacuousDall) =>
% 122.15/16.31                       (((quantDeMorgan1) =>
% 122.15/16.31                         (((quantDeMorgan2) =>
% 122.15/16.31                           (((quantDeMorgan3) =>
% 122.15/16.31                             (((quantDeMorgan4) =>
% 122.15/16.31                               (((prop2setI) =>
% 122.15/16.31                                 (((prop2set2propI) =>
% 122.15/16.31                                   (((notdexE) =>
% 122.15/16.31                                     (((notdallE) =>
% 122.15/16.31                                       (((exuI1) =>
% 122.15/16.31                                         (((exuI3) =>
% 122.15/16.31                                           (((exuI2) =>
% 122.15/16.31                                             (((inCongP) =>
% 122.15/16.31                                               (((in__Cong) =>
% 122.15/16.31                                                 (((exuE3u) =>
% 122.15/16.31                                                   (((exu__Cong) =>
% 122.15/16.31                                                     (((setadjoin__Cong) =>
% 122.15/16.31                                                       (((powerset__Cong) =>
% 122.15/16.31                                                         (((setunion__Cong) =>
% 122.15/16.31                                                           (((exuEu) =>
% 122.15/16.31                                                             (((descr__Cong) =>
% 122.15/16.31                                                               (((dsetconstr__Cong) =>
% 122.15/16.31                                                                 (((subsetI1) =>
% 122.15/16.31                                                                   (((eqimpsubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqimpsubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (emptysetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notsubsetI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetRefl) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTrans) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subset2powerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetemptysetimpeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepInPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2IR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (disjointsetsI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (bs114d) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusERneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusELneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusILneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusIRneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (secondinupair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairiskpair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairsubunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairinpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsuniq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR11) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR12) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairequniteq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempaircEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrERa) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcImageSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (apProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (app) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (infuncsetfunc) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcinfuncset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcextLem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2lamEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrue) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueorfalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTELcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTERcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTnotintersectT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementImpComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contraSubsetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTcontraSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTILcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTIRcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTEcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule0) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1SetBreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (choice2fnsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compEex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionCommutes) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2W) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2A) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2B) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Equiv) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncInj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (leftInvIsSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjCantorThm) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (foundation2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSclos) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peano0notS) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peanoSinj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ordinalMinLem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (!!) @ (
% 122.15/16.31                                                                     ^[Y0 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (ordinal @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y1 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y2 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y2 @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ 
% 122.15/16.31                                                                      Y2) =>
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.31      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl406])).
% 122.15/16.31  thf(zip_derived_cl420, plain,
% 122.15/16.31      (~ (((singletonsswitch) =>
% 122.15/16.31           (((upairsetE) =>
% 122.15/16.31             (((upairsetIL) =>
% 122.15/16.31               (((upairsetIR) =>
% 122.15/16.31                 (((emptyE1) =>
% 122.15/16.31                   (((vacuousDall) =>
% 122.15/16.31                     (((quantDeMorgan1) =>
% 122.15/16.31                       (((quantDeMorgan2) =>
% 122.15/16.31                         (((quantDeMorgan3) =>
% 122.15/16.31                           (((quantDeMorgan4) =>
% 122.15/16.31                             (((prop2setI) =>
% 122.15/16.31                               (((prop2set2propI) =>
% 122.15/16.31                                 (((notdexE) =>
% 122.15/16.31                                   (((notdallE) =>
% 122.15/16.31                                     (((exuI1) =>
% 122.15/16.31                                       (((exuI3) =>
% 122.15/16.31                                         (((exuI2) =>
% 122.15/16.31                                           (((inCongP) =>
% 122.15/16.31                                             (((in__Cong) =>
% 122.15/16.31                                               (((exuE3u) =>
% 122.15/16.31                                                 (((exu__Cong) =>
% 122.15/16.31                                                   (((setadjoin__Cong) =>
% 122.15/16.31                                                     (((powerset__Cong) =>
% 122.15/16.31                                                       (((setunion__Cong) =>
% 122.15/16.31                                                         (((exuEu) =>
% 122.15/16.31                                                           (((descr__Cong) =>
% 122.15/16.31                                                             (((dsetconstr__Cong) =>
% 122.15/16.31                                                               (((subsetI1) =>
% 122.15/16.31                                                                 (((eqimpsubset2) =>
% 122.15/16.31                                                                   (((eqimpsubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (emptysetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notsubsetI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetRefl) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTrans) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subset2powerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetemptysetimpeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepInPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2IR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (disjointsetsI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (bs114d) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusERneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusELneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusILneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusIRneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (secondinupair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairiskpair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairsubunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairinpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsuniq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR11) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR12) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairequniteq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempaircEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrERa) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcImageSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (apProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (app) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (infuncsetfunc) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcinfuncset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcextLem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2lamEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrue) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueorfalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTELcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTERcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTnotintersectT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementImpComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contraSubsetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTcontraSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTILcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTIRcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTEcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule0) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1SetBreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (choice2fnsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compEex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionCommutes) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2W) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2A) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2B) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Equiv) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncInj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (leftInvIsSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjCantorThm) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (foundation2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSclos) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peano0notS) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peanoSinj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ordinalMinLem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (!!) @ (
% 122.15/16.31                                                                     ^[Y0 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (ordinal @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y1 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y2 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y2 @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ 
% 122.15/16.31                                                                      Y2) =>
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.31      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl413])).
% 122.15/16.31  thf(zip_derived_cl428, plain,
% 122.15/16.31      (~ (((upairsetE) =>
% 122.15/16.31           (((upairsetIL) =>
% 122.15/16.31             (((upairsetIR) =>
% 122.15/16.31               (((emptyE1) =>
% 122.15/16.31                 (((vacuousDall) =>
% 122.15/16.31                   (((quantDeMorgan1) =>
% 122.15/16.31                     (((quantDeMorgan2) =>
% 122.15/16.31                       (((quantDeMorgan3) =>
% 122.15/16.31                         (((quantDeMorgan4) =>
% 122.15/16.31                           (((prop2setI) =>
% 122.15/16.31                             (((prop2set2propI) =>
% 122.15/16.31                               (((notdexE) =>
% 122.15/16.31                                 (((notdallE) =>
% 122.15/16.31                                   (((exuI1) =>
% 122.15/16.31                                     (((exuI3) =>
% 122.15/16.31                                       (((exuI2) =>
% 122.15/16.31                                         (((inCongP) =>
% 122.15/16.31                                           (((in__Cong) =>
% 122.15/16.31                                             (((exuE3u) =>
% 122.15/16.31                                               (((exu__Cong) =>
% 122.15/16.31                                                 (((setadjoin__Cong) =>
% 122.15/16.31                                                   (((powerset__Cong) =>
% 122.15/16.31                                                     (((setunion__Cong) =>
% 122.15/16.31                                                       (((exuEu) =>
% 122.15/16.31                                                         (((descr__Cong) =>
% 122.15/16.31                                                           (((dsetconstr__Cong) =>
% 122.15/16.31                                                             (((subsetI1) =>
% 122.15/16.31                                                               (((eqimpsubset2) =>
% 122.15/16.31                                                                 (((eqimpsubset1) =>
% 122.15/16.31                                                                   (((subsetI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (emptysetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notsubsetI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetRefl) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTrans) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subset2powerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetemptysetimpeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepInPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2IR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (disjointsetsI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (bs114d) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusERneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusELneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusILneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusIRneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (secondinupair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairiskpair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairsubunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairinpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsuniq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR11) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR12) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairequniteq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempaircEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrERa) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcImageSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (apProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (app) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (infuncsetfunc) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcinfuncset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcextLem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2lamEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrue) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueorfalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTELcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectTERcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contrasubsetT3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (doubleComplementEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTnotintersectT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementImpComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (contraSubsetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementTcontraSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTILcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTIRcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionTEcontra) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2a) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2b) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (demorgan2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule0) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz13rule4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz1_5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1SetBreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (choice2fnsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1all1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1invE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1compEex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (breln1unionCommutes) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2W) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2A) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (woz2B) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Ex1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1Equiv) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (image1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (injFuncSetFuncInj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (leftInvIsSurj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (surjCantorThm) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (foundation2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notinself2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (omegaSclos) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peano0notS) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (peanoSinj) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (transitivesetOp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionTransitive) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ordinalMinLem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (!!) @ (
% 122.15/16.31                                                                     ^[Y0 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (ordinal @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y1 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (!!) @ (
% 122.15/16.31                                                                      ^[Y2 : $i]:
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y2 @ 
% 122.15/16.31                                                                      Y0) =>
% 122.15/16.31                                                                      ((
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ 
% 122.15/16.31                                                                      Y2) =>
% 122.15/16.31                                                                      (in @ 
% 122.15/16.31                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.31      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl420])).
% 122.15/16.31  thf(zip_derived_cl439, plain,
% 122.15/16.31      (~ (((upairsetIL) =>
% 122.15/16.31           (((upairsetIR) =>
% 122.15/16.31             (((emptyE1) =>
% 122.15/16.31               (((vacuousDall) =>
% 122.15/16.31                 (((quantDeMorgan1) =>
% 122.15/16.31                   (((quantDeMorgan2) =>
% 122.15/16.31                     (((quantDeMorgan3) =>
% 122.15/16.31                       (((quantDeMorgan4) =>
% 122.15/16.31                         (((prop2setI) =>
% 122.15/16.31                           (((prop2set2propI) =>
% 122.15/16.31                             (((notdexE) =>
% 122.15/16.31                               (((notdallE) =>
% 122.15/16.31                                 (((exuI1) =>
% 122.15/16.31                                   (((exuI3) =>
% 122.15/16.31                                     (((exuI2) =>
% 122.15/16.31                                       (((inCongP) =>
% 122.15/16.31                                         (((in__Cong) =>
% 122.15/16.31                                           (((exuE3u) =>
% 122.15/16.31                                             (((exu__Cong) =>
% 122.15/16.31                                               (((setadjoin__Cong) =>
% 122.15/16.31                                                 (((powerset__Cong) =>
% 122.15/16.31                                                   (((setunion__Cong) =>
% 122.15/16.31                                                     (((exuEu) =>
% 122.15/16.31                                                       (((descr__Cong) =>
% 122.15/16.31                                                         (((dsetconstr__Cong) =>
% 122.15/16.31                                                           (((subsetI1) =>
% 122.15/16.31                                                             (((eqimpsubset2) =>
% 122.15/16.31                                                               (((eqimpsubset1) =>
% 122.15/16.31                                                                 (((subsetI2) =>
% 122.15/16.31                                                                   (((emptysetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notsubsetI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (notequalI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetRefl) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTrans) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setadjoinSub2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subset2powerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetemptysetimpeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetE1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (inPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepInPowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (sepSubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2IR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionEcases) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset5) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (disjointsetsI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectRsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (bs114d) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusERneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusELneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusILneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusIRneg) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusLsub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusSubset1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffE) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffI2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (symdiffIneg2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (secondinupair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairIR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairiskpair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsubset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowerset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletoninpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairset2E) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairsubunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairinpowunion) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ubforcartprodlem3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempair) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionE2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setunionsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1I2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (singletonsuniq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theprop) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR11) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR12) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (upairequniteq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setukpairinjR) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndsingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ksndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (kpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndin) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemEL) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairmemER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodmempaircEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodfstpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodsndpairEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (cartprodpairsurjEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrSub) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setOfPairsIsBReln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrERa) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrEL2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (dpsetconstrER) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcImageSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (apProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (app) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (infuncsetfunc) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcinfuncset) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamProp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lamp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2p) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (brelnall2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ex1E2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp3) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcextLem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcGraphProp4) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eqbreln) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (funcext2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ap2apEq2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (lam2lamEq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (beta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (eta2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalseProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp1) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueProp2) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifSingleton) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (ifp) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (theeq) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrue) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iffalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (iftrueorfalse) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binintersectT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (binunionT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (powersetT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setminusT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (complementT_lem) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (setextT) =>
% 122.15/16.31                                                                     ((
% 122.15/16.31                                                                     (subsetTI) =>
% 122.15/16.31                                                                     ((
% 122.15/16.32                                                                     (powersetTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTELcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTERcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTnotintersectT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementImpComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contraSubsetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTcontraSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTILcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTIRcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTEcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule0) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1SetBreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (choice2fnsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compEex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionCommutes) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2W) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2A) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2B) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Equiv) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncInj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (leftInvIsSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjCantorThm) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (foundation2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSclos) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peano0notS) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peanoSinj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ordinalMinLem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (!!) @ (
% 122.15/16.32                                                                     ^[Y0 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (ordinal @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y1 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y2 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y2 @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ 
% 122.15/16.32                                                                      Y2) =>
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.32      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl428])).
% 122.15/16.32  thf(zip_derived_cl449, plain,
% 122.15/16.32      (~ (((upairsetIR) =>
% 122.15/16.32           (((emptyE1) =>
% 122.15/16.32             (((vacuousDall) =>
% 122.15/16.32               (((quantDeMorgan1) =>
% 122.15/16.32                 (((quantDeMorgan2) =>
% 122.15/16.32                   (((quantDeMorgan3) =>
% 122.15/16.32                     (((quantDeMorgan4) =>
% 122.15/16.32                       (((prop2setI) =>
% 122.15/16.32                         (((prop2set2propI) =>
% 122.15/16.32                           (((notdexE) =>
% 122.15/16.32                             (((notdallE) =>
% 122.15/16.32                               (((exuI1) =>
% 122.15/16.32                                 (((exuI3) =>
% 122.15/16.32                                   (((exuI2) =>
% 122.15/16.32                                     (((inCongP) =>
% 122.15/16.32                                       (((in__Cong) =>
% 122.15/16.32                                         (((exuE3u) =>
% 122.15/16.32                                           (((exu__Cong) =>
% 122.15/16.32                                             (((setadjoin__Cong) =>
% 122.15/16.32                                               (((powerset__Cong) =>
% 122.15/16.32                                                 (((setunion__Cong) =>
% 122.15/16.32                                                   (((exuEu) =>
% 122.15/16.32                                                     (((descr__Cong) =>
% 122.15/16.32                                                       (((dsetconstr__Cong) =>
% 122.15/16.32                                                         (((subsetI1) =>
% 122.15/16.32                                                           (((eqimpsubset2) =>
% 122.15/16.32                                                             (((eqimpsubset1) =>
% 122.15/16.32                                                               (((subsetI2) =>
% 122.15/16.32                                                                 (((emptysetsubset) =>
% 122.15/16.32                                                                   (((subsetE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetE2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notsubsetI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notequalI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notequalI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetRefl) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTrans) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subset2powerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetemptysetimpeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepInPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2IR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (disjointsetsI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (bs114d) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusERneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusELneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusILneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusIRneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (secondinupair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairiskpair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairsubunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairinpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionE2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsuniq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR11) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR12) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairequniteq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempaircEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrERa) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcImageSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (apProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (app) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (infuncsetfunc) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcinfuncset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcextLem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2lamEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrue) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueorfalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTELcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTERcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTnotintersectT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementImpComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contraSubsetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTcontraSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTILcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTIRcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTEcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule0) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1SetBreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (choice2fnsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compEex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionCommutes) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2W) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2A) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2B) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Equiv) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncInj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (leftInvIsSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjCantorThm) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (foundation2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSclos) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peano0notS) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peanoSinj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ordinalMinLem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (!!) @ (
% 122.15/16.32                                                                     ^[Y0 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (ordinal @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y1 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y2 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y2 @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ 
% 122.15/16.32                                                                      Y2) =>
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.32      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl439])).
% 122.15/16.32  thf(zip_derived_cl457, plain,
% 122.15/16.32      (~ (((emptyE1) =>
% 122.15/16.32           (((vacuousDall) =>
% 122.15/16.32             (((quantDeMorgan1) =>
% 122.15/16.32               (((quantDeMorgan2) =>
% 122.15/16.32                 (((quantDeMorgan3) =>
% 122.15/16.32                   (((quantDeMorgan4) =>
% 122.15/16.32                     (((prop2setI) =>
% 122.15/16.32                       (((prop2set2propI) =>
% 122.15/16.32                         (((notdexE) =>
% 122.15/16.32                           (((notdallE) =>
% 122.15/16.32                             (((exuI1) =>
% 122.15/16.32                               (((exuI3) =>
% 122.15/16.32                                 (((exuI2) =>
% 122.15/16.32                                   (((inCongP) =>
% 122.15/16.32                                     (((in__Cong) =>
% 122.15/16.32                                       (((exuE3u) =>
% 122.15/16.32                                         (((exu__Cong) =>
% 122.15/16.32                                           (((setadjoin__Cong) =>
% 122.15/16.32                                             (((powerset__Cong) =>
% 122.15/16.32                                               (((setunion__Cong) =>
% 122.15/16.32                                                 (((exuEu) =>
% 122.15/16.32                                                   (((descr__Cong) =>
% 122.15/16.32                                                     (((dsetconstr__Cong) =>
% 122.15/16.32                                                       (((subsetI1) =>
% 122.15/16.32                                                         (((eqimpsubset2) =>
% 122.15/16.32                                                           (((eqimpsubset1) =>
% 122.15/16.32                                                             (((subsetI2) =>
% 122.15/16.32                                                               (((emptysetsubset) =>
% 122.15/16.32                                                                 (((subsetE) =>
% 122.15/16.32                                                                   (((subsetE2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notsubsetI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notequalI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notequalI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetRefl) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTrans) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subset2powerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetemptysetimpeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepInPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2IR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (disjointsetsI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (bs114d) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusERneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusELneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusILneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusIRneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (secondinupair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairiskpair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairsubunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairinpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionE2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsuniq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR11) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR12) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairequniteq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempaircEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrERa) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcImageSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (apProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (app) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (infuncsetfunc) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcinfuncset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcextLem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2lamEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrue) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueorfalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTELcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTERcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTnotintersectT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementImpComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contraSubsetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTcontraSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTILcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTIRcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTEcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule0) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1SetBreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (choice2fnsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compEex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionCommutes) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2W) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2A) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2B) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Equiv) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncInj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (leftInvIsSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjCantorThm) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (foundation2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSclos) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peano0notS) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peanoSinj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ordinalMinLem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (!!) @ (
% 122.15/16.32                                                                     ^[Y0 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (ordinal @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y1 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y2 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y2 @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ 
% 122.15/16.32                                                                      Y2) =>
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.32      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl449])).
% 122.15/16.32  thf(zip_derived_cl465, plain,
% 122.15/16.32      (~ (((vacuousDall) =>
% 122.15/16.32           (((quantDeMorgan1) =>
% 122.15/16.32             (((quantDeMorgan2) =>
% 122.15/16.32               (((quantDeMorgan3) =>
% 122.15/16.32                 (((quantDeMorgan4) =>
% 122.15/16.32                   (((prop2setI) =>
% 122.15/16.32                     (((prop2set2propI) =>
% 122.15/16.32                       (((notdexE) =>
% 122.15/16.32                         (((notdallE) =>
% 122.15/16.32                           (((exuI1) =>
% 122.15/16.32                             (((exuI3) =>
% 122.15/16.32                               (((exuI2) =>
% 122.15/16.32                                 (((inCongP) =>
% 122.15/16.32                                   (((in__Cong) =>
% 122.15/16.32                                     (((exuE3u) =>
% 122.15/16.32                                       (((exu__Cong) =>
% 122.15/16.32                                         (((setadjoin__Cong) =>
% 122.15/16.32                                           (((powerset__Cong) =>
% 122.15/16.32                                             (((setunion__Cong) =>
% 122.15/16.32                                               (((exuEu) =>
% 122.15/16.32                                                 (((descr__Cong) =>
% 122.15/16.32                                                   (((dsetconstr__Cong) =>
% 122.15/16.32                                                     (((subsetI1) =>
% 122.15/16.32                                                       (((eqimpsubset2) =>
% 122.15/16.32                                                         (((eqimpsubset1) =>
% 122.15/16.32                                                           (((subsetI2) =>
% 122.15/16.32                                                             (((emptysetsubset) =>
% 122.15/16.32                                                               (((subsetE) =>
% 122.15/16.32                                                                 (((subsetE2) =>
% 122.15/16.32                                                                   (((notsubsetI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notequalI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notequalI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetRefl) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTrans) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subset2powerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetemptysetimpeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepInPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2IR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (disjointsetsI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (bs114d) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusERneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusELneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusILneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusIRneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (secondinupair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairiskpair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairsubunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairinpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionE2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsuniq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR11) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR12) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairequniteq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempaircEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrERa) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcImageSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (apProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (app) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (infuncsetfunc) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcinfuncset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcextLem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2lamEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrue) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueorfalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTELcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTERcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTnotintersectT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementImpComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contraSubsetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTcontraSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTILcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTIRcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTEcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule0) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1SetBreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (choice2fnsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compEex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionCommutes) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2W) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2A) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2B) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Equiv) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncInj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (leftInvIsSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjCantorThm) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (foundation2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSclos) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peano0notS) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peanoSinj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ordinalMinLem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (!!) @ (
% 122.15/16.32                                                                     ^[Y0 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (ordinal @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y1 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y2 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y2 @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ 
% 122.15/16.32                                                                      Y2) =>
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.32      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl457])).
% 122.15/16.32  thf(zip_derived_cl471, plain,
% 122.15/16.32      (~ (((quantDeMorgan1) =>
% 122.15/16.32           (((quantDeMorgan2) =>
% 122.15/16.32             (((quantDeMorgan3) =>
% 122.15/16.32               (((quantDeMorgan4) =>
% 122.15/16.32                 (((prop2setI) =>
% 122.15/16.32                   (((prop2set2propI) =>
% 122.15/16.32                     (((notdexE) =>
% 122.15/16.32                       (((notdallE) =>
% 122.15/16.32                         (((exuI1) =>
% 122.15/16.32                           (((exuI3) =>
% 122.15/16.32                             (((exuI2) =>
% 122.15/16.32                               (((inCongP) =>
% 122.15/16.32                                 (((in__Cong) =>
% 122.15/16.32                                   (((exuE3u) =>
% 122.15/16.32                                     (((exu__Cong) =>
% 122.15/16.32                                       (((setadjoin__Cong) =>
% 122.15/16.32                                         (((powerset__Cong) =>
% 122.15/16.32                                           (((setunion__Cong) =>
% 122.15/16.32                                             (((exuEu) =>
% 122.15/16.32                                               (((descr__Cong) =>
% 122.15/16.32                                                 (((dsetconstr__Cong) =>
% 122.15/16.32                                                   (((subsetI1) =>
% 122.15/16.32                                                     (((eqimpsubset2) =>
% 122.15/16.32                                                       (((eqimpsubset1) =>
% 122.15/16.32                                                         (((subsetI2) =>
% 122.15/16.32                                                           (((emptysetsubset) =>
% 122.15/16.32                                                             (((subsetE) =>
% 122.15/16.32                                                               (((subsetE2) =>
% 122.15/16.32                                                                 (((notsubsetI) =>
% 122.15/16.32                                                                   (((notequalI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notequalI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetRefl) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTrans) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subset2powerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetemptysetimpeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepInPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2IR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (disjointsetsI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (bs114d) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusERneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusELneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusILneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusIRneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (secondinupair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairiskpair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairsubunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairinpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionE2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsuniq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR11) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR12) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairequniteq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempaircEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrERa) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcImageSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (apProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (app) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (infuncsetfunc) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcinfuncset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcextLem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2lamEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrue) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueorfalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTELcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTERcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTnotintersectT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementImpComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contraSubsetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTcontraSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTILcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTIRcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTEcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule0) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1SetBreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (choice2fnsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compEex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionCommutes) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2W) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2A) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2B) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Equiv) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncInj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (leftInvIsSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjCantorThm) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (foundation2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSclos) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peano0notS) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peanoSinj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ordinalMinLem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (!!) @ (
% 122.15/16.32                                                                     ^[Y0 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (ordinal @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y1 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y2 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y2 @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ 
% 122.15/16.32                                                                      Y2) =>
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.32      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl465])).
% 122.15/16.32  thf(zip_derived_cl478, plain,
% 122.15/16.32      (~ (((quantDeMorgan2) =>
% 122.15/16.32           (((quantDeMorgan3) =>
% 122.15/16.32             (((quantDeMorgan4) =>
% 122.15/16.32               (((prop2setI) =>
% 122.15/16.32                 (((prop2set2propI) =>
% 122.15/16.32                   (((notdexE) =>
% 122.15/16.32                     (((notdallE) =>
% 122.15/16.32                       (((exuI1) =>
% 122.15/16.32                         (((exuI3) =>
% 122.15/16.32                           (((exuI2) =>
% 122.15/16.32                             (((inCongP) =>
% 122.15/16.32                               (((in__Cong) =>
% 122.15/16.32                                 (((exuE3u) =>
% 122.15/16.32                                   (((exu__Cong) =>
% 122.15/16.32                                     (((setadjoin__Cong) =>
% 122.15/16.32                                       (((powerset__Cong) =>
% 122.15/16.32                                         (((setunion__Cong) =>
% 122.15/16.32                                           (((exuEu) =>
% 122.15/16.32                                             (((descr__Cong) =>
% 122.15/16.32                                               (((dsetconstr__Cong) =>
% 122.15/16.32                                                 (((subsetI1) =>
% 122.15/16.32                                                   (((eqimpsubset2) =>
% 122.15/16.32                                                     (((eqimpsubset1) =>
% 122.15/16.32                                                       (((subsetI2) =>
% 122.15/16.32                                                         (((emptysetsubset) =>
% 122.15/16.32                                                           (((subsetE) =>
% 122.15/16.32                                                             (((subsetE2) =>
% 122.15/16.32                                                               (((notsubsetI) =>
% 122.15/16.32                                                                 (((notequalI1) =>
% 122.15/16.32                                                                   (((notequalI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetRefl) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTrans) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subset2powerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetemptysetimpeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepInPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2IR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (disjointsetsI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (bs114d) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusERneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusELneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusILneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusIRneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (secondinupair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairiskpair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairsubunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairinpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionE2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsuniq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR11) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR12) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairequniteq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempaircEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrERa) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcImageSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (apProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (app) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (infuncsetfunc) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcinfuncset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcextLem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2lamEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrue) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueorfalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTELcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTERcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTnotintersectT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementImpComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contraSubsetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTcontraSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTILcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTIRcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTEcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule0) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1SetBreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (choice2fnsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compEex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionCommutes) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2W) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2A) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2B) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Equiv) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncInj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (leftInvIsSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjCantorThm) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (foundation2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSclos) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peano0notS) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peanoSinj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ordinalMinLem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (!!) @ (
% 122.15/16.32                                                                     ^[Y0 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (ordinal @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y1 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y2 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y2 @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ 
% 122.15/16.32                                                                      Y2) =>
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.32      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl471])).
% 122.15/16.32  thf(zip_derived_cl484, plain,
% 122.15/16.32      (~ (((quantDeMorgan3) =>
% 122.15/16.32           (((quantDeMorgan4) =>
% 122.15/16.32             (((prop2setI) =>
% 122.15/16.32               (((prop2set2propI) =>
% 122.15/16.32                 (((notdexE) =>
% 122.15/16.32                   (((notdallE) =>
% 122.15/16.32                     (((exuI1) =>
% 122.15/16.32                       (((exuI3) =>
% 122.15/16.32                         (((exuI2) =>
% 122.15/16.32                           (((inCongP) =>
% 122.15/16.32                             (((in__Cong) =>
% 122.15/16.32                               (((exuE3u) =>
% 122.15/16.32                                 (((exu__Cong) =>
% 122.15/16.32                                   (((setadjoin__Cong) =>
% 122.15/16.32                                     (((powerset__Cong) =>
% 122.15/16.32                                       (((setunion__Cong) =>
% 122.15/16.32                                         (((exuEu) =>
% 122.15/16.32                                           (((descr__Cong) =>
% 122.15/16.32                                             (((dsetconstr__Cong) =>
% 122.15/16.32                                               (((subsetI1) =>
% 122.15/16.32                                                 (((eqimpsubset2) =>
% 122.15/16.32                                                   (((eqimpsubset1) =>
% 122.15/16.32                                                     (((subsetI2) =>
% 122.15/16.32                                                       (((emptysetsubset) =>
% 122.15/16.32                                                         (((subsetE) =>
% 122.15/16.32                                                           (((subsetE2) =>
% 122.15/16.32                                                             (((notsubsetI) =>
% 122.15/16.32                                                               (((notequalI1) =>
% 122.15/16.32                                                                 (((notequalI2) =>
% 122.15/16.32                                                                   (((subsetRefl) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTrans) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subset2powerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetemptysetimpeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepInPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2IR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (disjointsetsI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (bs114d) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusERneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusELneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusILneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusIRneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (secondinupair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairiskpair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairsubunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairinpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionE2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsuniq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR11) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR12) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairequniteq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempaircEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrERa) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcImageSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (apProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (app) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (infuncsetfunc) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcinfuncset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcextLem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2lamEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrue) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueorfalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTELcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTERcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTnotintersectT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementImpComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contraSubsetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTcontraSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTILcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTIRcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTEcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule0) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1SetBreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (choice2fnsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compEex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionCommutes) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2W) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2A) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2B) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Equiv) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncInj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (leftInvIsSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjCantorThm) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (foundation2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSclos) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peano0notS) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peanoSinj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ordinalMinLem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (!!) @ (
% 122.15/16.32                                                                     ^[Y0 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (ordinal @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y1 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y2 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y2 @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ 
% 122.15/16.32                                                                      Y2) =>
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.32      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl478])).
% 122.15/16.32  thf(zip_derived_cl491, plain,
% 122.15/16.32      (~ (((quantDeMorgan4) =>
% 122.15/16.32           (((prop2setI) =>
% 122.15/16.32             (((prop2set2propI) =>
% 122.15/16.32               (((notdexE) =>
% 122.15/16.32                 (((notdallE) =>
% 122.15/16.32                   (((exuI1) =>
% 122.15/16.32                     (((exuI3) =>
% 122.15/16.32                       (((exuI2) =>
% 122.15/16.32                         (((inCongP) =>
% 122.15/16.32                           (((in__Cong) =>
% 122.15/16.32                             (((exuE3u) =>
% 122.15/16.32                               (((exu__Cong) =>
% 122.15/16.32                                 (((setadjoin__Cong) =>
% 122.15/16.32                                   (((powerset__Cong) =>
% 122.15/16.32                                     (((setunion__Cong) =>
% 122.15/16.32                                       (((exuEu) =>
% 122.15/16.32                                         (((descr__Cong) =>
% 122.15/16.32                                           (((dsetconstr__Cong) =>
% 122.15/16.32                                             (((subsetI1) =>
% 122.15/16.32                                               (((eqimpsubset2) =>
% 122.15/16.32                                                 (((eqimpsubset1) =>
% 122.15/16.32                                                   (((subsetI2) =>
% 122.15/16.32                                                     (((emptysetsubset) =>
% 122.15/16.32                                                       (((subsetE) =>
% 122.15/16.32                                                         (((subsetE2) =>
% 122.15/16.32                                                           (((notsubsetI) =>
% 122.15/16.32                                                             (((notequalI1) =>
% 122.15/16.32                                                               (((notequalI2) =>
% 122.15/16.32                                                                 (((subsetRefl) =>
% 122.15/16.32                                                                   (((subsetTrans) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subset2powerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetemptysetimpeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepInPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2IR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (disjointsetsI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (bs114d) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusERneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusELneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusILneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusIRneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (secondinupair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairiskpair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairsubunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairinpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionE2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsuniq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR11) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR12) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairequniteq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempaircEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrERa) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcImageSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (apProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (app) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (infuncsetfunc) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcinfuncset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcextLem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2lamEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrue) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueorfalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTELcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTERcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTnotintersectT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementImpComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contraSubsetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTcontraSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTILcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTIRcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTEcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule0) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1SetBreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (choice2fnsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compEex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionCommutes) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2W) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2A) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2B) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Equiv) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncInj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (leftInvIsSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjCantorThm) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (foundation2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSclos) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peano0notS) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peanoSinj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ordinalMinLem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (!!) @ (
% 122.15/16.32                                                                     ^[Y0 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (ordinal @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y1 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y2 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y2 @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ 
% 122.15/16.32                                                                      Y2) =>
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.32      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl484])).
% 122.15/16.32  thf(zip_derived_cl501, plain,
% 122.15/16.32      (~ (((prop2setI) =>
% 122.15/16.32           (((prop2set2propI) =>
% 122.15/16.32             (((notdexE) =>
% 122.15/16.32               (((notdallE) =>
% 122.15/16.32                 (((exuI1) =>
% 122.15/16.32                   (((exuI3) =>
% 122.15/16.32                     (((exuI2) =>
% 122.15/16.32                       (((inCongP) =>
% 122.15/16.32                         (((in__Cong) =>
% 122.15/16.32                           (((exuE3u) =>
% 122.15/16.32                             (((exu__Cong) =>
% 122.15/16.32                               (((setadjoin__Cong) =>
% 122.15/16.32                                 (((powerset__Cong) =>
% 122.15/16.32                                   (((setunion__Cong) =>
% 122.15/16.32                                     (((exuEu) =>
% 122.15/16.32                                       (((descr__Cong) =>
% 122.15/16.32                                         (((dsetconstr__Cong) =>
% 122.15/16.32                                           (((subsetI1) =>
% 122.15/16.32                                             (((eqimpsubset2) =>
% 122.15/16.32                                               (((eqimpsubset1) =>
% 122.15/16.32                                                 (((subsetI2) =>
% 122.15/16.32                                                   (((emptysetsubset) =>
% 122.15/16.32                                                     (((subsetE) =>
% 122.15/16.32                                                       (((subsetE2) =>
% 122.15/16.32                                                         (((notsubsetI) =>
% 122.15/16.32                                                           (((notequalI1) =>
% 122.15/16.32                                                             (((notequalI2) =>
% 122.15/16.32                                                               (((subsetRefl) =>
% 122.15/16.32                                                                 (((subsetTrans) =>
% 122.15/16.32                                                                   (((setadjoinSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setadjoinSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subset2powerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetemptysetimpeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepInPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2IR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (disjointsetsI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (bs114d) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusERneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusELneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusILneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusIRneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (secondinupair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairiskpair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairsubunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairinpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionE2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsuniq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR11) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR12) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairequniteq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempaircEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrERa) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcImageSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (apProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (app) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (infuncsetfunc) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcinfuncset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcextLem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2lamEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrue) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueorfalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTELcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTERcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTnotintersectT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementImpComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contraSubsetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTcontraSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTILcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTIRcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTEcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule0) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1SetBreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (choice2fnsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compEex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionCommutes) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2W) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2A) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2B) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Equiv) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncInj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (leftInvIsSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjCantorThm) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (foundation2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSclos) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peano0notS) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peanoSinj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ordinalMinLem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (!!) @ (
% 122.15/16.32                                                                     ^[Y0 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (ordinal @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y1 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y2 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y2 @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ 
% 122.15/16.32                                                                      Y2) =>
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.32      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl491])).
% 122.15/16.32  thf(zip_derived_cl508, plain,
% 122.15/16.32      (~ (((prop2set2propI) =>
% 122.15/16.32           (((notdexE) =>
% 122.15/16.32             (((notdallE) =>
% 122.15/16.32               (((exuI1) =>
% 122.15/16.32                 (((exuI3) =>
% 122.15/16.32                   (((exuI2) =>
% 122.15/16.32                     (((inCongP) =>
% 122.15/16.32                       (((in__Cong) =>
% 122.15/16.32                         (((exuE3u) =>
% 122.15/16.32                           (((exu__Cong) =>
% 122.15/16.32                             (((setadjoin__Cong) =>
% 122.15/16.32                               (((powerset__Cong) =>
% 122.15/16.32                                 (((setunion__Cong) =>
% 122.15/16.32                                   (((exuEu) =>
% 122.15/16.32                                     (((descr__Cong) =>
% 122.15/16.32                                       (((dsetconstr__Cong) =>
% 122.15/16.32                                         (((subsetI1) =>
% 122.15/16.32                                           (((eqimpsubset2) =>
% 122.15/16.32                                             (((eqimpsubset1) =>
% 122.15/16.32                                               (((subsetI2) =>
% 122.15/16.32                                                 (((emptysetsubset) =>
% 122.15/16.32                                                   (((subsetE) =>
% 122.15/16.32                                                     (((subsetE2) =>
% 122.15/16.32                                                       (((notsubsetI) =>
% 122.15/16.32                                                         (((notequalI1) =>
% 122.15/16.32                                                           (((notequalI2) =>
% 122.15/16.32                                                             (((subsetRefl) =>
% 122.15/16.32                                                               (((subsetTrans) =>
% 122.15/16.32                                                                 (((setadjoinSub) =>
% 122.15/16.32                                                                   (((setadjoinSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subset2powerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetemptysetimpeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepInPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2IR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (disjointsetsI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (bs114d) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusERneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusELneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusILneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusIRneg) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffI2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (symdiffIneg2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (secondinupair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairiskpair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletoninpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairsubunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairinpowunion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ubforcartprodlem3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempair) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionE2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1I2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (singletonsuniq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR11) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR12) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairequniteq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setukpairinjR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ksndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (kpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndin) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairmemER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodmempaircEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodfstpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodsndpairEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (cartprodpairsurjEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrSub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrERa) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrEL2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (dpsetconstrER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcImageSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (apProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (app) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (infuncsetfunc) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcinfuncset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamProp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lamp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2p) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (brelnall2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ex1E2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcextLem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcGraphProp4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (funcext2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ap2apEq2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (lam2lamEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (beta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eta2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalseProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueProp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifSingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ifp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (theeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrue) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iffalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (iftrueorfalse) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementT_lem) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetTI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTELcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectTERcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contrasubsetT3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementSub2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (doubleComplementEq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTnotintersectT) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementImpComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (contraSubsetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementTcontraSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTILcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTIRcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionTEcontra) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2a) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2b) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (demorgan2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule0) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz13rule4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz1_5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1SetBreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (choice2fnsingleton) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1all1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (eqbreln1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1invE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1compEex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionprop) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (breln1unionCommutes) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2W) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2A) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (woz2B) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Ex1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1Equiv) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1E) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (image1I) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (injFuncSetFuncInj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (leftInvIsSurj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (surjCantorThm) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (foundation2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (notinself2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSp) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (omegaSclos) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peano0notS) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (peanoSinj) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (transitivesetOp2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setunionTransitive) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (ordinalMinLem1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (!!) @ (
% 122.15/16.32                                                                     ^[Y0 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (ordinal @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y1 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (!!) @ (
% 122.15/16.32                                                                      ^[Y2 : $i]:
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y2 @ 
% 122.15/16.32                                                                      Y0) =>
% 122.15/16.32                                                                      ((
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ 
% 122.15/16.32                                                                      Y2) =>
% 122.15/16.32                                                                      (in @ 
% 122.15/16.32                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.32      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl501])).
% 122.15/16.32  thf(zip_derived_cl515, plain,
% 122.15/16.32      (~ (((notdexE) =>
% 122.15/16.32           (((notdallE) =>
% 122.15/16.32             (((exuI1) =>
% 122.15/16.32               (((exuI3) =>
% 122.15/16.32                 (((exuI2) =>
% 122.15/16.32                   (((inCongP) =>
% 122.15/16.32                     (((in__Cong) =>
% 122.15/16.32                       (((exuE3u) =>
% 122.15/16.32                         (((exu__Cong) =>
% 122.15/16.32                           (((setadjoin__Cong) =>
% 122.15/16.32                             (((powerset__Cong) =>
% 122.15/16.32                               (((setunion__Cong) =>
% 122.15/16.32                                 (((exuEu) =>
% 122.15/16.32                                   (((descr__Cong) =>
% 122.15/16.32                                     (((dsetconstr__Cong) =>
% 122.15/16.32                                       (((subsetI1) =>
% 122.15/16.32                                         (((eqimpsubset2) =>
% 122.15/16.32                                           (((eqimpsubset1) =>
% 122.15/16.32                                             (((subsetI2) =>
% 122.15/16.32                                               (((emptysetsubset) =>
% 122.15/16.32                                                 (((subsetE) =>
% 122.15/16.32                                                   (((subsetE2) =>
% 122.15/16.32                                                     (((notsubsetI) =>
% 122.15/16.32                                                       (((notequalI1) =>
% 122.15/16.32                                                         (((notequalI2) =>
% 122.15/16.32                                                           (((subsetRefl) =>
% 122.15/16.32                                                             (((subsetTrans) =>
% 122.15/16.32                                                               (((setadjoinSub) =>
% 122.15/16.32                                                                 (((setadjoinSub2) =>
% 122.15/16.32                                                                   (((subset2powerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setextsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (subsetemptysetimpeq) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetE1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (inPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (powersetsubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepInPowerset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (sepSubset) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (upairset2IR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionIR) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionEcases) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionE) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binunionRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset5) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectEL) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectLsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset2) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset3) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectER) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (disjointsetsI1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectRsub) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset4) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (binintersectSubset1) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (bs114d) =>
% 122.15/16.32                                                                     ((
% 122.15/16.32                                                                     (setminusI) =>
% 122.15/16.32                                                                     ((
% 122.15/16.33                                                                     (setminusEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusERneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusELneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusILneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusIRneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (secondinupair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairiskpair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairsubunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairinpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionE2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsuniq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR11) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR12) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairequniteq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempaircEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrSub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrERa) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcImageSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (apProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (app) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (infuncsetfunc) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcinfuncset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcextLem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2lamEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theeq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrue) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueorfalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setextT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subsetTI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTELcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTERcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTnotintersectT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementImpComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contraSubsetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTcontraSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTILcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTIRcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTEcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule0) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1SetBreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (choice2fnsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compEex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionCommutes) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2W) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2A) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2B) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Equiv) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncInj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (leftInvIsSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjCantorThm) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (foundation2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSclos) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peano0notS) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peanoSinj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ordinalMinLem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (!!) @ (
% 122.15/16.33                                                                     ^[Y0 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (ordinal @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y1 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y2 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y2 @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ 
% 122.15/16.33                                                                      Y2) =>
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.33      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl508])).
% 122.15/16.33  thf(zip_derived_cl523, plain,
% 122.15/16.33      (~ (((notdallE) =>
% 122.15/16.33           (((exuI1) =>
% 122.15/16.33             (((exuI3) =>
% 122.15/16.33               (((exuI2) =>
% 122.15/16.33                 (((inCongP) =>
% 122.15/16.33                   (((in__Cong) =>
% 122.15/16.33                     (((exuE3u) =>
% 122.15/16.33                       (((exu__Cong) =>
% 122.15/16.33                         (((setadjoin__Cong) =>
% 122.15/16.33                           (((powerset__Cong) =>
% 122.15/16.33                             (((setunion__Cong) =>
% 122.15/16.33                               (((exuEu) =>
% 122.15/16.33                                 (((descr__Cong) =>
% 122.15/16.33                                   (((dsetconstr__Cong) =>
% 122.15/16.33                                     (((subsetI1) =>
% 122.15/16.33                                       (((eqimpsubset2) =>
% 122.15/16.33                                         (((eqimpsubset1) =>
% 122.15/16.33                                           (((subsetI2) =>
% 122.15/16.33                                             (((emptysetsubset) =>
% 122.15/16.33                                               (((subsetE) =>
% 122.15/16.33                                                 (((subsetE2) =>
% 122.15/16.33                                                   (((notsubsetI) =>
% 122.15/16.33                                                     (((notequalI1) =>
% 122.15/16.33                                                       (((notequalI2) =>
% 122.15/16.33                                                         (((subsetRefl) =>
% 122.15/16.33                                                           (((subsetTrans) =>
% 122.15/16.33                                                             (((setadjoinSub) =>
% 122.15/16.33                                                               (((setadjoinSub2) =>
% 122.15/16.33                                                                 (((subset2powerset) =>
% 122.15/16.33                                                                   (((setextsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subsetemptysetimpeq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inPowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepInPowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2IR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (disjointsetsI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (bs114d) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusERneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusELneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusILneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusIRneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (secondinupair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairiskpair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairsubunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairinpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionE2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsuniq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR11) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR12) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairequniteq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempaircEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrSub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrERa) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcImageSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (apProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (app) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (infuncsetfunc) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcinfuncset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcextLem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2lamEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theeq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrue) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueorfalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setextT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subsetTI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTELcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTERcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTnotintersectT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementImpComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contraSubsetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTcontraSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTILcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTIRcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTEcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule0) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1SetBreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (choice2fnsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compEex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionCommutes) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2W) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2A) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2B) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Equiv) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncInj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (leftInvIsSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjCantorThm) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (foundation2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSclos) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peano0notS) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peanoSinj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ordinalMinLem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (!!) @ (
% 122.15/16.33                                                                     ^[Y0 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (ordinal @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y1 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y2 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y2 @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ 
% 122.15/16.33                                                                      Y2) =>
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.33      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl515])).
% 122.15/16.33  thf(zip_derived_cl535, plain,
% 122.15/16.33      (~ (((exuI1) =>
% 122.15/16.33           (((exuI3) =>
% 122.15/16.33             (((exuI2) =>
% 122.15/16.33               (((inCongP) =>
% 122.15/16.33                 (((in__Cong) =>
% 122.15/16.33                   (((exuE3u) =>
% 122.15/16.33                     (((exu__Cong) =>
% 122.15/16.33                       (((setadjoin__Cong) =>
% 122.15/16.33                         (((powerset__Cong) =>
% 122.15/16.33                           (((setunion__Cong) =>
% 122.15/16.33                             (((exuEu) =>
% 122.15/16.33                               (((descr__Cong) =>
% 122.15/16.33                                 (((dsetconstr__Cong) =>
% 122.15/16.33                                   (((subsetI1) =>
% 122.15/16.33                                     (((eqimpsubset2) =>
% 122.15/16.33                                       (((eqimpsubset1) =>
% 122.15/16.33                                         (((subsetI2) =>
% 122.15/16.33                                           (((emptysetsubset) =>
% 122.15/16.33                                             (((subsetE) =>
% 122.15/16.33                                               (((subsetE2) =>
% 122.15/16.33                                                 (((notsubsetI) =>
% 122.15/16.33                                                   (((notequalI1) =>
% 122.15/16.33                                                     (((notequalI2) =>
% 122.15/16.33                                                       (((subsetRefl) =>
% 122.15/16.33                                                         (((subsetTrans) =>
% 122.15/16.33                                                           (((setadjoinSub) =>
% 122.15/16.33                                                             (((setadjoinSub2) =>
% 122.15/16.33                                                               (((subset2powerset) =>
% 122.15/16.33                                                                 (((setextsub) =>
% 122.15/16.33                                                                   (((subsetemptysetimpeq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inPowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepInPowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2IR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (disjointsetsI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (bs114d) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusERneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusELneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusILneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusIRneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (secondinupair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairiskpair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairsubunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairinpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionE2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsuniq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR11) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR12) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairequniteq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempaircEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrSub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrERa) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcImageSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (apProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (app) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (infuncsetfunc) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcinfuncset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcextLem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2lamEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theeq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrue) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueorfalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setextT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subsetTI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTELcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTERcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTnotintersectT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementImpComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contraSubsetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTcontraSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTILcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTIRcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTEcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule0) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1SetBreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (choice2fnsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compEex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionCommutes) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2W) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2A) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2B) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Equiv) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncInj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (leftInvIsSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjCantorThm) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (foundation2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSclos) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peano0notS) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peanoSinj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ordinalMinLem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (!!) @ (
% 122.15/16.33                                                                     ^[Y0 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (ordinal @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y1 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y2 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y2 @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ 
% 122.15/16.33                                                                      Y2) =>
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.33      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl523])).
% 122.15/16.33  thf(zip_derived_cl550, plain,
% 122.15/16.33      (~ (((exuI3) =>
% 122.15/16.33           (((exuI2) =>
% 122.15/16.33             (((inCongP) =>
% 122.15/16.33               (((in__Cong) =>
% 122.15/16.33                 (((exuE3u) =>
% 122.15/16.33                   (((exu__Cong) =>
% 122.15/16.33                     (((setadjoin__Cong) =>
% 122.15/16.33                       (((powerset__Cong) =>
% 122.15/16.33                         (((setunion__Cong) =>
% 122.15/16.33                           (((exuEu) =>
% 122.15/16.33                             (((descr__Cong) =>
% 122.15/16.33                               (((dsetconstr__Cong) =>
% 122.15/16.33                                 (((subsetI1) =>
% 122.15/16.33                                   (((eqimpsubset2) =>
% 122.15/16.33                                     (((eqimpsubset1) =>
% 122.15/16.33                                       (((subsetI2) =>
% 122.15/16.33                                         (((emptysetsubset) =>
% 122.15/16.33                                           (((subsetE) =>
% 122.15/16.33                                             (((subsetE2) =>
% 122.15/16.33                                               (((notsubsetI) =>
% 122.15/16.33                                                 (((notequalI1) =>
% 122.15/16.33                                                   (((notequalI2) =>
% 122.15/16.33                                                     (((subsetRefl) =>
% 122.15/16.33                                                       (((subsetTrans) =>
% 122.15/16.33                                                         (((setadjoinSub) =>
% 122.15/16.33                                                           (((setadjoinSub2) =>
% 122.15/16.33                                                             (((subset2powerset) =>
% 122.15/16.33                                                               (((setextsub) =>
% 122.15/16.33                                                                 (((subsetemptysetimpeq) =>
% 122.15/16.33                                                                   (((powersetI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inPowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepInPowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2IR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (disjointsetsI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (bs114d) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusERneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusELneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusILneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusIRneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (secondinupair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairiskpair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairsubunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairinpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionE2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsuniq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR11) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR12) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairequniteq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempaircEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrSub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrERa) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcImageSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (apProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (app) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (infuncsetfunc) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcinfuncset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcextLem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2lamEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theeq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrue) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueorfalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setextT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subsetTI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTELcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTERcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTnotintersectT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementImpComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contraSubsetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTcontraSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTILcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTIRcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTEcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule0) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1SetBreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (choice2fnsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compEex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionCommutes) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2W) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2A) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2B) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Equiv) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncInj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (leftInvIsSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjCantorThm) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (foundation2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSclos) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peano0notS) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peanoSinj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ordinalMinLem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (!!) @ (
% 122.15/16.33                                                                     ^[Y0 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (ordinal @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y1 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y2 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y2 @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ 
% 122.15/16.33                                                                      Y2) =>
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.33      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl535])).
% 122.15/16.33  thf(zip_derived_cl560, plain,
% 122.15/16.33      (~ (((exuI2) =>
% 122.15/16.33           (((inCongP) =>
% 122.15/16.33             (((in__Cong) =>
% 122.15/16.33               (((exuE3u) =>
% 122.15/16.33                 (((exu__Cong) =>
% 122.15/16.33                   (((setadjoin__Cong) =>
% 122.15/16.33                     (((powerset__Cong) =>
% 122.15/16.33                       (((setunion__Cong) =>
% 122.15/16.33                         (((exuEu) =>
% 122.15/16.33                           (((descr__Cong) =>
% 122.15/16.33                             (((dsetconstr__Cong) =>
% 122.15/16.33                               (((subsetI1) =>
% 122.15/16.33                                 (((eqimpsubset2) =>
% 122.15/16.33                                   (((eqimpsubset1) =>
% 122.15/16.33                                     (((subsetI2) =>
% 122.15/16.33                                       (((emptysetsubset) =>
% 122.15/16.33                                         (((subsetE) =>
% 122.15/16.33                                           (((subsetE2) =>
% 122.15/16.33                                             (((notsubsetI) =>
% 122.15/16.33                                               (((notequalI1) =>
% 122.15/16.33                                                 (((notequalI2) =>
% 122.15/16.33                                                   (((subsetRefl) =>
% 122.15/16.33                                                     (((subsetTrans) =>
% 122.15/16.33                                                       (((setadjoinSub) =>
% 122.15/16.33                                                         (((setadjoinSub2) =>
% 122.15/16.33                                                           (((subset2powerset) =>
% 122.15/16.33                                                             (((setextsub) =>
% 122.15/16.33                                                               (((subsetemptysetimpeq) =>
% 122.15/16.33                                                                 (((powersetI1) =>
% 122.15/16.33                                                                   (((powersetE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inPowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepInPowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2IR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (disjointsetsI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (bs114d) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusERneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusELneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusILneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusIRneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (secondinupair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairiskpair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairsubunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairinpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionE2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsuniq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR11) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR12) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairequniteq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempaircEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrSub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrERa) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcImageSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (apProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (app) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (infuncsetfunc) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcinfuncset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcextLem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2lamEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theeq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrue) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueorfalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setextT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subsetTI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTELcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTERcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTnotintersectT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementImpComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contraSubsetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTcontraSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTILcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTIRcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTEcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule0) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1SetBreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (choice2fnsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compEex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionCommutes) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2W) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2A) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2B) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Equiv) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncInj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (leftInvIsSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjCantorThm) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (foundation2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSclos) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peano0notS) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peanoSinj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ordinalMinLem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (!!) @ (
% 122.15/16.33                                                                     ^[Y0 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (ordinal @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y1 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y2 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y2 @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ 
% 122.15/16.33                                                                      Y2) =>
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.33      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl550])).
% 122.15/16.33  thf(zip_derived_cl568, plain,
% 122.15/16.33      (~ (((inCongP) =>
% 122.15/16.33           (((in__Cong) =>
% 122.15/16.33             (((exuE3u) =>
% 122.15/16.33               (((exu__Cong) =>
% 122.15/16.33                 (((setadjoin__Cong) =>
% 122.15/16.33                   (((powerset__Cong) =>
% 122.15/16.33                     (((setunion__Cong) =>
% 122.15/16.33                       (((exuEu) =>
% 122.15/16.33                         (((descr__Cong) =>
% 122.15/16.33                           (((dsetconstr__Cong) =>
% 122.15/16.33                             (((subsetI1) =>
% 122.15/16.33                               (((eqimpsubset2) =>
% 122.15/16.33                                 (((eqimpsubset1) =>
% 122.15/16.33                                   (((subsetI2) =>
% 122.15/16.33                                     (((emptysetsubset) =>
% 122.15/16.33                                       (((subsetE) =>
% 122.15/16.33                                         (((subsetE2) =>
% 122.15/16.33                                           (((notsubsetI) =>
% 122.15/16.33                                             (((notequalI1) =>
% 122.15/16.33                                               (((notequalI2) =>
% 122.15/16.33                                                 (((subsetRefl) =>
% 122.15/16.33                                                   (((subsetTrans) =>
% 122.15/16.33                                                     (((setadjoinSub) =>
% 122.15/16.33                                                       (((setadjoinSub2) =>
% 122.15/16.33                                                         (((subset2powerset) =>
% 122.15/16.33                                                           (((setextsub) =>
% 122.15/16.33                                                             (((subsetemptysetimpeq) =>
% 122.15/16.33                                                               (((powersetI1) =>
% 122.15/16.33                                                                 (((powersetE1) =>
% 122.15/16.33                                                                   (((inPowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepInPowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2IR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (disjointsetsI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (bs114d) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusERneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusELneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusILneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusIRneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (secondinupair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairiskpair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairsubunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairinpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionE2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsuniq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR11) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR12) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairequniteq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempaircEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrSub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrERa) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcImageSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (apProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (app) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (infuncsetfunc) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcinfuncset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcextLem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2lamEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theeq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrue) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueorfalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setextT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subsetTI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTELcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTERcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTnotintersectT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementImpComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contraSubsetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTcontraSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTILcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTIRcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTEcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule0) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1SetBreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (choice2fnsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compEex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionCommutes) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2W) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2A) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2B) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Equiv) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncInj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (leftInvIsSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjCantorThm) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (foundation2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSclos) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peano0notS) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peanoSinj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ordinalMinLem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (!!) @ (
% 122.15/16.33                                                                     ^[Y0 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (ordinal @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y1 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y2 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y2 @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ 
% 122.15/16.33                                                                      Y2) =>
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.33      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl560])).
% 122.15/16.33  thf(zip_derived_cl578, plain,
% 122.15/16.33      (~ (((in__Cong) =>
% 122.15/16.33           (((exuE3u) =>
% 122.15/16.33             (((exu__Cong) =>
% 122.15/16.33               (((setadjoin__Cong) =>
% 122.15/16.33                 (((powerset__Cong) =>
% 122.15/16.33                   (((setunion__Cong) =>
% 122.15/16.33                     (((exuEu) =>
% 122.15/16.33                       (((descr__Cong) =>
% 122.15/16.33                         (((dsetconstr__Cong) =>
% 122.15/16.33                           (((subsetI1) =>
% 122.15/16.33                             (((eqimpsubset2) =>
% 122.15/16.33                               (((eqimpsubset1) =>
% 122.15/16.33                                 (((subsetI2) =>
% 122.15/16.33                                   (((emptysetsubset) =>
% 122.15/16.33                                     (((subsetE) =>
% 122.15/16.33                                       (((subsetE2) =>
% 122.15/16.33                                         (((notsubsetI) =>
% 122.15/16.33                                           (((notequalI1) =>
% 122.15/16.33                                             (((notequalI2) =>
% 122.15/16.33                                               (((subsetRefl) =>
% 122.15/16.33                                                 (((subsetTrans) =>
% 122.15/16.33                                                   (((setadjoinSub) =>
% 122.15/16.33                                                     (((setadjoinSub2) =>
% 122.15/16.33                                                       (((subset2powerset) =>
% 122.15/16.33                                                         (((setextsub) =>
% 122.15/16.33                                                           (((subsetemptysetimpeq) =>
% 122.15/16.33                                                             (((powersetI1) =>
% 122.15/16.33                                                               (((powersetE1) =>
% 122.15/16.33                                                                 (((inPowerset) =>
% 122.15/16.33                                                                   (((powersetsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepInPowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2IR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (disjointsetsI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (bs114d) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusERneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusELneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusILneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusIRneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (secondinupair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairiskpair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairsubunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairinpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionE2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsuniq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR11) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR12) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairequniteq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempaircEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrSub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrERa) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcImageSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (apProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (app) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (infuncsetfunc) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcinfuncset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcextLem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2lamEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theeq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrue) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueorfalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setextT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subsetTI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTELcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTERcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTnotintersectT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementImpComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contraSubsetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTcontraSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTILcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTIRcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTEcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule0) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1SetBreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (choice2fnsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compEex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionCommutes) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2W) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2A) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2B) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Equiv) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncInj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (leftInvIsSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjCantorThm) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (foundation2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSclos) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peano0notS) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peanoSinj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ordinalMinLem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (!!) @ (
% 122.15/16.33                                                                     ^[Y0 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (ordinal @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y1 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y2 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y2 @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ 
% 122.15/16.33                                                                      Y2) =>
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.33      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl568])).
% 122.15/16.33  thf(zip_derived_cl588, plain,
% 122.15/16.33      (~ (((exuE3u) =>
% 122.15/16.33           (((exu__Cong) =>
% 122.15/16.33             (((setadjoin__Cong) =>
% 122.15/16.33               (((powerset__Cong) =>
% 122.15/16.33                 (((setunion__Cong) =>
% 122.15/16.33                   (((exuEu) =>
% 122.15/16.33                     (((descr__Cong) =>
% 122.15/16.33                       (((dsetconstr__Cong) =>
% 122.15/16.33                         (((subsetI1) =>
% 122.15/16.33                           (((eqimpsubset2) =>
% 122.15/16.33                             (((eqimpsubset1) =>
% 122.15/16.33                               (((subsetI2) =>
% 122.15/16.33                                 (((emptysetsubset) =>
% 122.15/16.33                                   (((subsetE) =>
% 122.15/16.33                                     (((subsetE2) =>
% 122.15/16.33                                       (((notsubsetI) =>
% 122.15/16.33                                         (((notequalI1) =>
% 122.15/16.33                                           (((notequalI2) =>
% 122.15/16.33                                             (((subsetRefl) =>
% 122.15/16.33                                               (((subsetTrans) =>
% 122.15/16.33                                                 (((setadjoinSub) =>
% 122.15/16.33                                                   (((setadjoinSub2) =>
% 122.15/16.33                                                     (((subset2powerset) =>
% 122.15/16.33                                                       (((setextsub) =>
% 122.15/16.33                                                         (((subsetemptysetimpeq) =>
% 122.15/16.33                                                           (((powersetI1) =>
% 122.15/16.33                                                             (((powersetE1) =>
% 122.15/16.33                                                               (((inPowerset) =>
% 122.15/16.33                                                                 (((powersetsubset) =>
% 122.15/16.33                                                                   (((sepInPowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (sepSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2IR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (disjointsetsI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (bs114d) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusERneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusELneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusILneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusIRneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (secondinupair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairiskpair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairsubunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairinpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionE2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsuniq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR11) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR12) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairequniteq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempaircEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrSub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrERa) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcImageSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (apProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (app) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (infuncsetfunc) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcinfuncset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcextLem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2lamEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theeq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrue) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueorfalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setextT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subsetTI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTELcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTERcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTnotintersectT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementImpComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contraSubsetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTcontraSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTILcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTIRcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTEcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule0) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1SetBreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (choice2fnsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compEex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionCommutes) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2W) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2A) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2B) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Equiv) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncInj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (leftInvIsSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjCantorThm) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (foundation2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSclos) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peano0notS) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peanoSinj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ordinalMinLem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (!!) @ (
% 122.15/16.33                                                                     ^[Y0 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (ordinal @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y1 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y2 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y2 @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ 
% 122.15/16.33                                                                      Y2) =>
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.33      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl578])).
% 122.15/16.33  thf(zip_derived_cl598, plain,
% 122.15/16.33      (~ (((exu__Cong) =>
% 122.15/16.33           (((setadjoin__Cong) =>
% 122.15/16.33             (((powerset__Cong) =>
% 122.15/16.33               (((setunion__Cong) =>
% 122.15/16.33                 (((exuEu) =>
% 122.15/16.33                   (((descr__Cong) =>
% 122.15/16.33                     (((dsetconstr__Cong) =>
% 122.15/16.33                       (((subsetI1) =>
% 122.15/16.33                         (((eqimpsubset2) =>
% 122.15/16.33                           (((eqimpsubset1) =>
% 122.15/16.33                             (((subsetI2) =>
% 122.15/16.33                               (((emptysetsubset) =>
% 122.15/16.33                                 (((subsetE) =>
% 122.15/16.33                                   (((subsetE2) =>
% 122.15/16.33                                     (((notsubsetI) =>
% 122.15/16.33                                       (((notequalI1) =>
% 122.15/16.33                                         (((notequalI2) =>
% 122.15/16.33                                           (((subsetRefl) =>
% 122.15/16.33                                             (((subsetTrans) =>
% 122.15/16.33                                               (((setadjoinSub) =>
% 122.15/16.33                                                 (((setadjoinSub2) =>
% 122.15/16.33                                                   (((subset2powerset) =>
% 122.15/16.33                                                     (((setextsub) =>
% 122.15/16.33                                                       (((subsetemptysetimpeq) =>
% 122.15/16.33                                                         (((powersetI1) =>
% 122.15/16.33                                                           (((powersetE1) =>
% 122.15/16.33                                                             (((inPowerset) =>
% 122.15/16.33                                                               (((powersetsubset) =>
% 122.15/16.33                                                                 (((sepInPowerset) =>
% 122.15/16.33                                                                   (((sepSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2IR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (disjointsetsI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (bs114d) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusERneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusELneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusILneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusIRneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (secondinupair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairiskpair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairsubunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairinpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionE2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsuniq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR11) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR12) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairequniteq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempaircEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrSub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrERa) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcImageSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (apProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (app) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (infuncsetfunc) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcinfuncset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcextLem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2lamEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theeq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrue) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueorfalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setextT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subsetTI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTELcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTERcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTnotintersectT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementImpComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contraSubsetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTcontraSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTILcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTIRcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTEcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule0) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1SetBreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (choice2fnsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compEex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionCommutes) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2W) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2A) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2B) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Equiv) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncInj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (leftInvIsSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjCantorThm) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (foundation2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSclos) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peano0notS) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peanoSinj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ordinalMinLem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (!!) @ (
% 122.15/16.33                                                                     ^[Y0 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (ordinal @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y1 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y2 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y2 @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ 
% 122.15/16.33                                                                      Y2) =>
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.33      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl588])).
% 122.15/16.33  thf(zip_derived_cl609, plain,
% 122.15/16.33      (~ (((setadjoin__Cong) =>
% 122.15/16.33           (((powerset__Cong) =>
% 122.15/16.33             (((setunion__Cong) =>
% 122.15/16.33               (((exuEu) =>
% 122.15/16.33                 (((descr__Cong) =>
% 122.15/16.33                   (((dsetconstr__Cong) =>
% 122.15/16.33                     (((subsetI1) =>
% 122.15/16.33                       (((eqimpsubset2) =>
% 122.15/16.33                         (((eqimpsubset1) =>
% 122.15/16.33                           (((subsetI2) =>
% 122.15/16.33                             (((emptysetsubset) =>
% 122.15/16.33                               (((subsetE) =>
% 122.15/16.33                                 (((subsetE2) =>
% 122.15/16.33                                   (((notsubsetI) =>
% 122.15/16.33                                     (((notequalI1) =>
% 122.15/16.33                                       (((notequalI2) =>
% 122.15/16.33                                         (((subsetRefl) =>
% 122.15/16.33                                           (((subsetTrans) =>
% 122.15/16.33                                             (((setadjoinSub) =>
% 122.15/16.33                                               (((setadjoinSub2) =>
% 122.15/16.33                                                 (((subset2powerset) =>
% 122.15/16.33                                                   (((setextsub) =>
% 122.15/16.33                                                     (((subsetemptysetimpeq) =>
% 122.15/16.33                                                       (((powersetI1) =>
% 122.15/16.33                                                         (((powersetE1) =>
% 122.15/16.33                                                           (((inPowerset) =>
% 122.15/16.33                                                             (((powersetsubset) =>
% 122.15/16.33                                                               (((sepInPowerset) =>
% 122.15/16.33                                                                 (((sepSubset) =>
% 122.15/16.33                                                                   (((binunionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2IR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (disjointsetsI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectRsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (bs114d) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusERneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusELneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusILneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusIRneg) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusLsub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusSubset1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffI2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (symdiffIneg2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (secondinupair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairiskpair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowerset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletoninpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairset2E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairsubunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairinpowunion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ubforcartprodlem3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempair) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionE2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1I2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (singletonsuniq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR11) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR12) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (upairequniteq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setukpairinjR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ksndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (kpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndin) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemEL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairmemER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodmempaircEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodfstpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodsndpairEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (cartprodpairsurjEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrSub) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrERa) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrEL2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (dpsetconstrER) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcImageSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (apProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (app) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (infuncsetfunc) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcinfuncset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamProp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lamp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2p) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (brelnall2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ex1E2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcextLem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcGraphProp4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (funcext2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ap2apEq2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (lam2lamEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (beta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eta2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalseProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueProp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifSingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ifp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (theeq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrue) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iffalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (iftrueorfalse) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setminusT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementT_lem) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setextT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subsetTI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (powersetTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTELcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintersectTERcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contrasubsetT3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementI1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementE1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementSub2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (doubleComplementEq) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTnotintersectT) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementImpComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (contraSubsetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementTcontraSubset) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTILcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTIRcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binunionTEcontra) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2a) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2b) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (demorgan2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule0) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz13rule4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_3) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_4) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz1_5) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1SetBreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (choice2fnsingleton) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1all1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (subbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (eqbreln1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1invE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1compEex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionprop) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIL) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionIR) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionI) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionE) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionEcases) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (breln1unionCommutes) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2W) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2A) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (woz2B) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Ex1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1Equiv) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1E) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (image1I) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (injFuncSetFuncInj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (leftInvIsSurj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (surjCantorThm) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (foundation2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (notinself2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSp) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (omegaSclos) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peano0notS) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (peanoSinj) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (binintTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (transitivesetOp2) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (setunionTransitive) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (ordinalMinLem1) =>
% 122.15/16.33                                                                     ((
% 122.15/16.33                                                                     (!!) @ (
% 122.15/16.33                                                                     ^[Y0 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (ordinal @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y1 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (!!) @ (
% 122.15/16.33                                                                      ^[Y2 : $i]:
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y2 @ 
% 122.15/16.33                                                                      Y0) =>
% 122.15/16.33                                                                      ((
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ 
% 122.15/16.33                                                                      Y2) =>
% 122.15/16.33                                                                      (in @ 
% 122.15/16.33                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.33      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl598])).
% 122.15/16.33  thf(zip_derived_cl623, plain,
% 122.15/16.33      (~ (((powerset__Cong) =>
% 122.15/16.33           (((setunion__Cong) =>
% 122.15/16.33             (((exuEu) =>
% 122.15/16.33               (((descr__Cong) =>
% 122.15/16.33                 (((dsetconstr__Cong) =>
% 122.15/16.33                   (((subsetI1) =>
% 122.15/16.33                     (((eqimpsubset2) =>
% 122.15/16.33                       (((eqimpsubset1) =>
% 122.15/16.33                         (((subsetI2) =>
% 122.15/16.33                           (((emptysetsubset) =>
% 122.15/16.33                             (((subsetE) =>
% 122.15/16.33                               (((subsetE2) =>
% 122.15/16.33                                 (((notsubsetI) =>
% 122.15/16.33                                   (((notequalI1) =>
% 122.15/16.33                                     (((notequalI2) =>
% 122.15/16.33                                       (((subsetRefl) =>
% 122.15/16.33                                         (((subsetTrans) =>
% 122.15/16.33                                           (((setadjoinSub) =>
% 122.15/16.33                                             (((setadjoinSub2) =>
% 122.15/16.33                                               (((subset2powerset) =>
% 122.15/16.33                                                 (((setextsub) =>
% 122.15/16.33                                                   (((subsetemptysetimpeq) =>
% 122.15/16.33                                                     (((powersetI1) =>
% 122.15/16.33                                                       (((powersetE1) =>
% 122.15/16.34                                                         (((inPowerset) =>
% 122.15/16.34                                                           (((powersetsubset) =>
% 122.15/16.34                                                             (((sepInPowerset) =>
% 122.15/16.34                                                               (((sepSubset) =>
% 122.15/16.34                                                                 (((binunionIL) =>
% 122.15/16.34                                                                   (((upairset2IR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (disjointsetsI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (bs114d) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusERneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusELneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusILneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusIRneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (secondinupair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairiskpair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowerset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairset2E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairsubunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairinpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionE2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsuniq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR11) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR12) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairequniteq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempaircEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrSub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrERa) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcImageSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (apProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (app) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (infuncsetfunc) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcinfuncset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcextLem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2lamEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theeq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrue) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueorfalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setextT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subsetTI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTELcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTERcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTnotintersectT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementImpComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contraSubsetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTcontraSubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTILcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTIRcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTEcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule0) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1SetBreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (choice2fnsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compEex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionCommutes) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2W) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2A) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2B) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Equiv) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncInj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (leftInvIsSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjCantorThm) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (foundation2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSclos) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peano0notS) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peanoSinj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ordinalMinLem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (!!) @ (
% 122.15/16.34                                                                     ^[Y0 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (ordinal @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y1 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y2 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y2 @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ 
% 122.15/16.34                                                                      Y2) =>
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.34      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl609])).
% 122.15/16.34  thf(zip_derived_cl637, plain,
% 122.15/16.34      (~ (((setunion__Cong) =>
% 122.15/16.34           (((exuEu) =>
% 122.15/16.34             (((descr__Cong) =>
% 122.15/16.34               (((dsetconstr__Cong) =>
% 122.15/16.34                 (((subsetI1) =>
% 122.15/16.34                   (((eqimpsubset2) =>
% 122.15/16.34                     (((eqimpsubset1) =>
% 122.15/16.34                       (((subsetI2) =>
% 122.15/16.34                         (((emptysetsubset) =>
% 122.15/16.34                           (((subsetE) =>
% 122.15/16.34                             (((subsetE2) =>
% 122.15/16.34                               (((notsubsetI) =>
% 122.15/16.34                                 (((notequalI1) =>
% 122.15/16.34                                   (((notequalI2) =>
% 122.15/16.34                                     (((subsetRefl) =>
% 122.15/16.34                                       (((subsetTrans) =>
% 122.15/16.34                                         (((setadjoinSub) =>
% 122.15/16.34                                           (((setadjoinSub2) =>
% 122.15/16.34                                             (((subset2powerset) =>
% 122.15/16.34                                               (((setextsub) =>
% 122.15/16.34                                                 (((subsetemptysetimpeq) =>
% 122.15/16.34                                                   (((powersetI1) =>
% 122.15/16.34                                                     (((powersetE1) =>
% 122.15/16.34                                                       (((inPowerset) =>
% 122.15/16.34                                                         (((powersetsubset) =>
% 122.15/16.34                                                           (((sepInPowerset) =>
% 122.15/16.34                                                             (((sepSubset) =>
% 122.15/16.34                                                               (((binunionIL) =>
% 122.15/16.34                                                                 (((upairset2IR) =>
% 122.15/16.34                                                                   (((binunionIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (disjointsetsI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (bs114d) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusERneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusELneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusILneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusIRneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (secondinupair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairiskpair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowerset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairset2E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairsubunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairinpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionE2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsuniq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR11) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR12) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairequniteq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempaircEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrSub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrERa) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcImageSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (apProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (app) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (infuncsetfunc) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcinfuncset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcextLem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2lamEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theeq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrue) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueorfalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setextT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subsetTI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTELcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTERcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTnotintersectT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementImpComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contraSubsetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTcontraSubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTILcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTIRcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTEcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule0) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1SetBreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (choice2fnsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compEex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionCommutes) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2W) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2A) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2B) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Equiv) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncInj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (leftInvIsSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjCantorThm) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (foundation2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSclos) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peano0notS) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peanoSinj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ordinalMinLem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (!!) @ (
% 122.15/16.34                                                                     ^[Y0 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (ordinal @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y1 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y2 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y2 @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ 
% 122.15/16.34                                                                      Y2) =>
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.34      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl623])).
% 122.15/16.34  thf(zip_derived_cl652, plain,
% 122.15/16.34      (~ (((exuEu) =>
% 122.15/16.34           (((descr__Cong) =>
% 122.15/16.34             (((dsetconstr__Cong) =>
% 122.15/16.34               (((subsetI1) =>
% 122.15/16.34                 (((eqimpsubset2) =>
% 122.15/16.34                   (((eqimpsubset1) =>
% 122.15/16.34                     (((subsetI2) =>
% 122.15/16.34                       (((emptysetsubset) =>
% 122.15/16.34                         (((subsetE) =>
% 122.15/16.34                           (((subsetE2) =>
% 122.15/16.34                             (((notsubsetI) =>
% 122.15/16.34                               (((notequalI1) =>
% 122.15/16.34                                 (((notequalI2) =>
% 122.15/16.34                                   (((subsetRefl) =>
% 122.15/16.34                                     (((subsetTrans) =>
% 122.15/16.34                                       (((setadjoinSub) =>
% 122.15/16.34                                         (((setadjoinSub2) =>
% 122.15/16.34                                           (((subset2powerset) =>
% 122.15/16.34                                             (((setextsub) =>
% 122.15/16.34                                               (((subsetemptysetimpeq) =>
% 122.15/16.34                                                 (((powersetI1) =>
% 122.15/16.34                                                   (((powersetE1) =>
% 122.15/16.34                                                     (((inPowerset) =>
% 122.15/16.34                                                       (((powersetsubset) =>
% 122.15/16.34                                                         (((sepInPowerset) =>
% 122.15/16.34                                                           (((sepSubset) =>
% 122.15/16.34                                                             (((binunionIL) =>
% 122.15/16.34                                                               (((upairset2IR) =>
% 122.15/16.34                                                                 (((binunionIR) =>
% 122.15/16.34                                                                   (((binunionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (disjointsetsI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (bs114d) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusERneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusELneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusILneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusIRneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (secondinupair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairiskpair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowerset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairset2E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairsubunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairinpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionE2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsuniq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR11) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR12) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairequniteq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempaircEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrSub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrERa) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcImageSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (apProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (app) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (infuncsetfunc) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcinfuncset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcextLem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2lamEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theeq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrue) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueorfalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setextT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subsetTI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTELcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTERcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTnotintersectT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementImpComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contraSubsetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTcontraSubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTILcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTIRcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTEcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule0) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1SetBreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (choice2fnsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compEex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionCommutes) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2W) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2A) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2B) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Equiv) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncInj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (leftInvIsSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjCantorThm) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (foundation2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSclos) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peano0notS) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peanoSinj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ordinalMinLem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (!!) @ (
% 122.15/16.34                                                                     ^[Y0 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (ordinal @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y1 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y2 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y2 @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ 
% 122.15/16.34                                                                      Y2) =>
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.34      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl637])).
% 122.15/16.34  thf(zip_derived_cl664, plain,
% 122.15/16.34      (~ (((descr__Cong) =>
% 122.15/16.34           (((dsetconstr__Cong) =>
% 122.15/16.34             (((subsetI1) =>
% 122.15/16.34               (((eqimpsubset2) =>
% 122.15/16.34                 (((eqimpsubset1) =>
% 122.15/16.34                   (((subsetI2) =>
% 122.15/16.34                     (((emptysetsubset) =>
% 122.15/16.34                       (((subsetE) =>
% 122.15/16.34                         (((subsetE2) =>
% 122.15/16.34                           (((notsubsetI) =>
% 122.15/16.34                             (((notequalI1) =>
% 122.15/16.34                               (((notequalI2) =>
% 122.15/16.34                                 (((subsetRefl) =>
% 122.15/16.34                                   (((subsetTrans) =>
% 122.15/16.34                                     (((setadjoinSub) =>
% 122.15/16.34                                       (((setadjoinSub2) =>
% 122.15/16.34                                         (((subset2powerset) =>
% 122.15/16.34                                           (((setextsub) =>
% 122.15/16.34                                             (((subsetemptysetimpeq) =>
% 122.15/16.34                                               (((powersetI1) =>
% 122.15/16.34                                                 (((powersetE1) =>
% 122.15/16.34                                                   (((inPowerset) =>
% 122.15/16.34                                                     (((powersetsubset) =>
% 122.15/16.34                                                       (((sepInPowerset) =>
% 122.15/16.34                                                         (((sepSubset) =>
% 122.15/16.34                                                           (((binunionIL) =>
% 122.15/16.34                                                             (((upairset2IR) =>
% 122.15/16.34                                                               (((binunionIR) =>
% 122.15/16.34                                                                 (((binunionEcases) =>
% 122.15/16.34                                                                   (((binunionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (disjointsetsI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (bs114d) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusERneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusELneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusILneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusIRneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (secondinupair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairiskpair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowerset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairset2E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairsubunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairinpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionE2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsuniq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR11) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR12) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairequniteq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempaircEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrSub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrERa) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcImageSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (apProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (app) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (infuncsetfunc) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcinfuncset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcextLem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2lamEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theeq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrue) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueorfalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setextT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subsetTI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTELcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTERcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTnotintersectT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementImpComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contraSubsetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTcontraSubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTILcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTIRcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTEcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule0) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1SetBreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (choice2fnsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compEex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionCommutes) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2W) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2A) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2B) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Equiv) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncInj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (leftInvIsSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjCantorThm) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (foundation2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSclos) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peano0notS) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peanoSinj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ordinalMinLem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (!!) @ (
% 122.15/16.34                                                                     ^[Y0 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (ordinal @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y1 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y2 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y2 @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ 
% 122.15/16.34                                                                      Y2) =>
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.34      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl652])).
% 122.15/16.34  thf(zip_derived_cl681, plain,
% 122.15/16.34      (~ (((dsetconstr__Cong) =>
% 122.15/16.34           (((subsetI1) =>
% 122.15/16.34             (((eqimpsubset2) =>
% 122.15/16.34               (((eqimpsubset1) =>
% 122.15/16.34                 (((subsetI2) =>
% 122.15/16.34                   (((emptysetsubset) =>
% 122.15/16.34                     (((subsetE) =>
% 122.15/16.34                       (((subsetE2) =>
% 122.15/16.34                         (((notsubsetI) =>
% 122.15/16.34                           (((notequalI1) =>
% 122.15/16.34                             (((notequalI2) =>
% 122.15/16.34                               (((subsetRefl) =>
% 122.15/16.34                                 (((subsetTrans) =>
% 122.15/16.34                                   (((setadjoinSub) =>
% 122.15/16.34                                     (((setadjoinSub2) =>
% 122.15/16.34                                       (((subset2powerset) =>
% 122.15/16.34                                         (((setextsub) =>
% 122.15/16.34                                           (((subsetemptysetimpeq) =>
% 122.15/16.34                                             (((powersetI1) =>
% 122.15/16.34                                               (((powersetE1) =>
% 122.15/16.34                                                 (((inPowerset) =>
% 122.15/16.34                                                   (((powersetsubset) =>
% 122.15/16.34                                                     (((sepInPowerset) =>
% 122.15/16.34                                                       (((sepSubset) =>
% 122.15/16.34                                                         (((binunionIL) =>
% 122.15/16.34                                                           (((upairset2IR) =>
% 122.15/16.34                                                             (((binunionIR) =>
% 122.15/16.34                                                               (((binunionEcases) =>
% 122.15/16.34                                                                 (((binunionE) =>
% 122.15/16.34                                                                   (((binunionLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (disjointsetsI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (bs114d) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusERneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusELneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusILneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusIRneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (secondinupair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairiskpair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowerset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairset2E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairsubunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairinpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionE2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsuniq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR11) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR12) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairequniteq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempaircEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrSub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrERa) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcImageSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (apProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (app) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (infuncsetfunc) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcinfuncset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcextLem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2lamEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theeq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrue) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueorfalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setextT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subsetTI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTELcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTERcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTnotintersectT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementImpComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contraSubsetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTcontraSubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTILcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTIRcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTEcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule0) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1SetBreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (choice2fnsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compEex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionCommutes) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2W) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2A) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2B) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Equiv) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncInj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (leftInvIsSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjCantorThm) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (foundation2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSclos) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peano0notS) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peanoSinj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ordinalMinLem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (!!) @ (
% 122.15/16.34                                                                     ^[Y0 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (ordinal @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y1 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y2 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y2 @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ 
% 122.15/16.34                                                                      Y2) =>
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.34      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl664])).
% 122.15/16.34  thf(zip_derived_cl698, plain,
% 122.15/16.34      (~ (((subsetI1) =>
% 122.15/16.34           (((eqimpsubset2) =>
% 122.15/16.34             (((eqimpsubset1) =>
% 122.15/16.34               (((subsetI2) =>
% 122.15/16.34                 (((emptysetsubset) =>
% 122.15/16.34                   (((subsetE) =>
% 122.15/16.34                     (((subsetE2) =>
% 122.15/16.34                       (((notsubsetI) =>
% 122.15/16.34                         (((notequalI1) =>
% 122.15/16.34                           (((notequalI2) =>
% 122.15/16.34                             (((subsetRefl) =>
% 122.15/16.34                               (((subsetTrans) =>
% 122.15/16.34                                 (((setadjoinSub) =>
% 122.15/16.34                                   (((setadjoinSub2) =>
% 122.15/16.34                                     (((subset2powerset) =>
% 122.15/16.34                                       (((setextsub) =>
% 122.15/16.34                                         (((subsetemptysetimpeq) =>
% 122.15/16.34                                           (((powersetI1) =>
% 122.15/16.34                                             (((powersetE1) =>
% 122.15/16.34                                               (((inPowerset) =>
% 122.15/16.34                                                 (((powersetsubset) =>
% 122.15/16.34                                                   (((sepInPowerset) =>
% 122.15/16.34                                                     (((sepSubset) =>
% 122.15/16.34                                                       (((binunionIL) =>
% 122.15/16.34                                                         (((upairset2IR) =>
% 122.15/16.34                                                           (((binunionIR) =>
% 122.15/16.34                                                             (((binunionEcases) =>
% 122.15/16.34                                                               (((binunionE) =>
% 122.15/16.34                                                                 (((binunionLsub) =>
% 122.15/16.34                                                                   (((binunionRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (disjointsetsI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (bs114d) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusERneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusELneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusILneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusIRneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (secondinupair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairiskpair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowerset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairset2E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairsubunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairinpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionE2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsuniq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR11) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR12) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairequniteq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempaircEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrSub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrERa) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcImageSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (apProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (app) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (infuncsetfunc) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcinfuncset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcextLem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2lamEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theeq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrue) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueorfalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setextT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subsetTI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTELcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTERcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTnotintersectT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementImpComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contraSubsetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTcontraSubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTILcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTIRcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTEcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule0) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1SetBreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (choice2fnsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compEex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionCommutes) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2W) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2A) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2B) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Equiv) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncInj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (leftInvIsSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjCantorThm) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (foundation2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSclos) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peano0notS) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peanoSinj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ordinalMinLem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (!!) @ (
% 122.15/16.34                                                                     ^[Y0 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (ordinal @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y1 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y2 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y2 @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ 
% 122.15/16.34                                                                      Y2) =>
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.34      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl681])).
% 122.15/16.34  thf(zip_derived_cl712, plain,
% 122.15/16.34      (~ (((eqimpsubset2) =>
% 122.15/16.34           (((eqimpsubset1) =>
% 122.15/16.34             (((subsetI2) =>
% 122.15/16.34               (((emptysetsubset) =>
% 122.15/16.34                 (((subsetE) =>
% 122.15/16.34                   (((subsetE2) =>
% 122.15/16.34                     (((notsubsetI) =>
% 122.15/16.34                       (((notequalI1) =>
% 122.15/16.34                         (((notequalI2) =>
% 122.15/16.34                           (((subsetRefl) =>
% 122.15/16.34                             (((subsetTrans) =>
% 122.15/16.34                               (((setadjoinSub) =>
% 122.15/16.34                                 (((setadjoinSub2) =>
% 122.15/16.34                                   (((subset2powerset) =>
% 122.15/16.34                                     (((setextsub) =>
% 122.15/16.34                                       (((subsetemptysetimpeq) =>
% 122.15/16.34                                         (((powersetI1) =>
% 122.15/16.34                                           (((powersetE1) =>
% 122.15/16.34                                             (((inPowerset) =>
% 122.15/16.34                                               (((powersetsubset) =>
% 122.15/16.34                                                 (((sepInPowerset) =>
% 122.15/16.34                                                   (((sepSubset) =>
% 122.15/16.34                                                     (((binunionIL) =>
% 122.15/16.34                                                       (((upairset2IR) =>
% 122.15/16.34                                                         (((binunionIR) =>
% 122.15/16.34                                                           (((binunionEcases) =>
% 122.15/16.34                                                             (((binunionE) =>
% 122.15/16.34                                                               (((binunionLsub) =>
% 122.15/16.34                                                                 (((binunionRsub) =>
% 122.15/16.34                                                                   (((binintersectI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (disjointsetsI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (bs114d) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusERneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusELneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusILneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusIRneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (secondinupair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairiskpair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowerset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairset2E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairsubunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairinpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionE2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsuniq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR11) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR12) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairequniteq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempaircEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrSub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrERa) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcImageSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (apProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (app) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (infuncsetfunc) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcinfuncset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcextLem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2lamEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theeq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrue) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueorfalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setextT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subsetTI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTELcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTERcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTnotintersectT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementImpComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contraSubsetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTcontraSubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTILcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTIRcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTEcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule0) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1SetBreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (choice2fnsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compEex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionCommutes) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2W) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2A) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2B) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Equiv) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncInj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (leftInvIsSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjCantorThm) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (foundation2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSclos) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peano0notS) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peanoSinj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ordinalMinLem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (!!) @ (
% 122.15/16.34                                                                     ^[Y0 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (ordinal @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y1 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y2 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y2 @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ 
% 122.15/16.34                                                                      Y2) =>
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.34      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl698])).
% 122.15/16.34  thf(zip_derived_cl725, plain,
% 122.15/16.34      (~ (((eqimpsubset1) =>
% 122.15/16.34           (((subsetI2) =>
% 122.15/16.34             (((emptysetsubset) =>
% 122.15/16.34               (((subsetE) =>
% 122.15/16.34                 (((subsetE2) =>
% 122.15/16.34                   (((notsubsetI) =>
% 122.15/16.34                     (((notequalI1) =>
% 122.15/16.34                       (((notequalI2) =>
% 122.15/16.34                         (((subsetRefl) =>
% 122.15/16.34                           (((subsetTrans) =>
% 122.15/16.34                             (((setadjoinSub) =>
% 122.15/16.34                               (((setadjoinSub2) =>
% 122.15/16.34                                 (((subset2powerset) =>
% 122.15/16.34                                   (((setextsub) =>
% 122.15/16.34                                     (((subsetemptysetimpeq) =>
% 122.15/16.34                                       (((powersetI1) =>
% 122.15/16.34                                         (((powersetE1) =>
% 122.15/16.34                                           (((inPowerset) =>
% 122.15/16.34                                             (((powersetsubset) =>
% 122.15/16.34                                               (((sepInPowerset) =>
% 122.15/16.34                                                 (((sepSubset) =>
% 122.15/16.34                                                   (((binunionIL) =>
% 122.15/16.34                                                     (((upairset2IR) =>
% 122.15/16.34                                                       (((binunionIR) =>
% 122.15/16.34                                                         (((binunionEcases) =>
% 122.15/16.34                                                           (((binunionE) =>
% 122.15/16.34                                                             (((binunionLsub) =>
% 122.15/16.34                                                               (((binunionRsub) =>
% 122.15/16.34                                                                 (((binintersectI) =>
% 122.15/16.34                                                                   (((binintersectSubset5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (disjointsetsI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (bs114d) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusERneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusELneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusILneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusIRneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (secondinupair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairiskpair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowerset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairset2E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairsubunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairinpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionE2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsuniq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR11) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR12) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairequniteq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempaircEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrSub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrERa) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcImageSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (apProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (app) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (infuncsetfunc) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcinfuncset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcextLem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2lamEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theeq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrue) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueorfalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setextT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subsetTI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTELcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTERcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTnotintersectT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementImpComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contraSubsetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTcontraSubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTILcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTIRcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTEcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule0) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1SetBreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (choice2fnsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compEex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionCommutes) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2W) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2A) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2B) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Equiv) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncInj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (leftInvIsSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjCantorThm) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (foundation2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSclos) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peano0notS) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peanoSinj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ordinalMinLem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (!!) @ (
% 122.15/16.34                                                                     ^[Y0 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (ordinal @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y1 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y2 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y2 @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ 
% 122.15/16.34                                                                      Y2) =>
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.34      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl712])).
% 122.15/16.34  thf(zip_derived_cl735, plain,
% 122.15/16.34      (~ (((subsetI2) =>
% 122.15/16.34           (((emptysetsubset) =>
% 122.15/16.34             (((subsetE) =>
% 122.15/16.34               (((subsetE2) =>
% 122.15/16.34                 (((notsubsetI) =>
% 122.15/16.34                   (((notequalI1) =>
% 122.15/16.34                     (((notequalI2) =>
% 122.15/16.34                       (((subsetRefl) =>
% 122.15/16.34                         (((subsetTrans) =>
% 122.15/16.34                           (((setadjoinSub) =>
% 122.15/16.34                             (((setadjoinSub2) =>
% 122.15/16.34                               (((subset2powerset) =>
% 122.15/16.34                                 (((setextsub) =>
% 122.15/16.34                                   (((subsetemptysetimpeq) =>
% 122.15/16.34                                     (((powersetI1) =>
% 122.15/16.34                                       (((powersetE1) =>
% 122.15/16.34                                         (((inPowerset) =>
% 122.15/16.34                                           (((powersetsubset) =>
% 122.15/16.34                                             (((sepInPowerset) =>
% 122.15/16.34                                               (((sepSubset) =>
% 122.15/16.34                                                 (((binunionIL) =>
% 122.15/16.34                                                   (((upairset2IR) =>
% 122.15/16.34                                                     (((binunionIR) =>
% 122.15/16.34                                                       (((binunionEcases) =>
% 122.15/16.34                                                         (((binunionE) =>
% 122.15/16.34                                                           (((binunionLsub) =>
% 122.15/16.34                                                             (((binunionRsub) =>
% 122.15/16.34                                                               (((binintersectI) =>
% 122.15/16.34                                                                 (((binintersectSubset5) =>
% 122.15/16.34                                                                   (((binintersectEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (disjointsetsI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (bs114d) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusERneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusELneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusILneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusIRneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (secondinupair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairiskpair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowerset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairset2E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairsubunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairinpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionE2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsuniq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR11) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR12) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairequniteq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempaircEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrSub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrERa) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcImageSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (apProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (app) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (infuncsetfunc) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcinfuncset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcextLem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2lamEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theeq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrue) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueorfalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setextT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subsetTI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTELcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTERcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTnotintersectT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementImpComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contraSubsetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTcontraSubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTILcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTIRcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTEcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule0) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1SetBreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (choice2fnsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compEex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionCommutes) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2W) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2A) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2B) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Equiv) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncInj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (leftInvIsSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjCantorThm) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (foundation2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSclos) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peano0notS) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peanoSinj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ordinalMinLem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (!!) @ (
% 122.15/16.34                                                                     ^[Y0 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (ordinal @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y1 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y2 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y2 @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ 
% 122.15/16.34                                                                      Y2) =>
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.34      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl725])).
% 122.15/16.34  thf(zip_derived_cl746, plain,
% 122.15/16.34      (~ (((emptysetsubset) =>
% 122.15/16.34           (((subsetE) =>
% 122.15/16.34             (((subsetE2) =>
% 122.15/16.34               (((notsubsetI) =>
% 122.15/16.34                 (((notequalI1) =>
% 122.15/16.34                   (((notequalI2) =>
% 122.15/16.34                     (((subsetRefl) =>
% 122.15/16.34                       (((subsetTrans) =>
% 122.15/16.34                         (((setadjoinSub) =>
% 122.15/16.34                           (((setadjoinSub2) =>
% 122.15/16.34                             (((subset2powerset) =>
% 122.15/16.34                               (((setextsub) =>
% 122.15/16.34                                 (((subsetemptysetimpeq) =>
% 122.15/16.34                                   (((powersetI1) =>
% 122.15/16.34                                     (((powersetE1) =>
% 122.15/16.34                                       (((inPowerset) =>
% 122.15/16.34                                         (((powersetsubset) =>
% 122.15/16.34                                           (((sepInPowerset) =>
% 122.15/16.34                                             (((sepSubset) =>
% 122.15/16.34                                               (((binunionIL) =>
% 122.15/16.34                                                 (((upairset2IR) =>
% 122.15/16.34                                                   (((binunionIR) =>
% 122.15/16.34                                                     (((binunionEcases) =>
% 122.15/16.34                                                       (((binunionE) =>
% 122.15/16.34                                                         (((binunionLsub) =>
% 122.15/16.34                                                           (((binunionRsub) =>
% 122.15/16.34                                                             (((binintersectI) =>
% 122.15/16.34                                                               (((binintersectSubset5) =>
% 122.15/16.34                                                                 (((binintersectEL) =>
% 122.15/16.34                                                                   (((binintersectLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (disjointsetsI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (bs114d) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusERneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusELneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusILneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusIRneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (secondinupair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairiskpair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowerset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairset2E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairsubunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairinpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionE2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsuniq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR11) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR12) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairequniteq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairmemER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempaircEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrSub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrERa) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrEL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (dpsetconstrER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcImageSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (apProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (app) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (infuncsetfunc) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcinfuncset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamProp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lamp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2p) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (brelnall2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcextLem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcGraphProp4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (funcext2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ap2apEq2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (lam2lamEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (beta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eta2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalseProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueProp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifSingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ifp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theeq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrue) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iffalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (iftrueorfalse) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementT_lem) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setextT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subsetTI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (powersetTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTELcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectTERcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contrasubsetT3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementE1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementSub2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (doubleComplementEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTnotintersectT) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementImpComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (contraSubsetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementTcontraSubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTILcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTIRcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binunionTEcontra) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2a) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2b) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (demorgan2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule0) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz13rule4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz1_5) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1SetBreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (choice2fnsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1all1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (subbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (eqbreln1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1invE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1compEex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionEcases) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (breln1unionCommutes) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2W) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2A) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (woz2B) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Ex1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1Equiv) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (image1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (injFuncSetFuncInj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (leftInvIsSurj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (surjCantorThm) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (foundation2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (notinself2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (omegaSclos) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peano0notS) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (peanoSinj) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (transitivesetOp2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionTransitive) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ordinalMinLem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (!!) @ (
% 122.15/16.34                                                                     ^[Y0 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (ordinal @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y1 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (!!) @ (
% 122.15/16.34                                                                      ^[Y2 : $i]:
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y2 @ 
% 122.15/16.34                                                                      Y0) =>
% 122.15/16.34                                                                      ((
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ 
% 122.15/16.34                                                                      Y2) =>
% 122.15/16.34                                                                      (in @ 
% 122.15/16.34                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.34      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl735])).
% 122.15/16.34  thf(zip_derived_cl758, plain,
% 122.15/16.34      (~ (((subsetE) =>
% 122.15/16.34           (((subsetE2) =>
% 122.15/16.34             (((notsubsetI) =>
% 122.15/16.34               (((notequalI1) =>
% 122.15/16.34                 (((notequalI2) =>
% 122.15/16.34                   (((subsetRefl) =>
% 122.15/16.34                     (((subsetTrans) =>
% 122.15/16.34                       (((setadjoinSub) =>
% 122.15/16.34                         (((setadjoinSub2) =>
% 122.15/16.34                           (((subset2powerset) =>
% 122.15/16.34                             (((setextsub) =>
% 122.15/16.34                               (((subsetemptysetimpeq) =>
% 122.15/16.34                                 (((powersetI1) =>
% 122.15/16.34                                   (((powersetE1) =>
% 122.15/16.34                                     (((inPowerset) =>
% 122.15/16.34                                       (((powersetsubset) =>
% 122.15/16.34                                         (((sepInPowerset) =>
% 122.15/16.34                                           (((sepSubset) =>
% 122.15/16.34                                             (((binunionIL) =>
% 122.15/16.34                                               (((upairset2IR) =>
% 122.15/16.34                                                 (((binunionIR) =>
% 122.15/16.34                                                   (((binunionEcases) =>
% 122.15/16.34                                                     (((binunionE) =>
% 122.15/16.34                                                       (((binunionLsub) =>
% 122.15/16.34                                                         (((binunionRsub) =>
% 122.15/16.34                                                           (((binintersectI) =>
% 122.15/16.34                                                             (((binintersectSubset5) =>
% 122.15/16.34                                                               (((binintersectEL) =>
% 122.15/16.34                                                                 (((binintersectLsub) =>
% 122.15/16.34                                                                   (((binintersectSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (disjointsetsI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectRsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset4) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (binintersectSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (bs114d) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusI) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusEL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusER) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusERneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusELneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusILneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusIRneg) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusLsub) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setminusSubset1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffE) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffI2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (symdiffIneg2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (secondinupair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairIR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairiskpair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairp) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsubset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowerset) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletoninpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairset2E) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairsubunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairinpowunion) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ubforcartprodlem3) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodpairin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodmempair) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionE2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setunionsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1E1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ex1I2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (singletonsuniq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (theprop) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kfstpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodfstin) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjL) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR11) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR12) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR1) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (upairequniteq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR2) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (setukpairinjR) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndsingleton) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (ksndpairEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (kpairsurjEq) =>
% 122.15/16.34                                                                     ((
% 122.15/16.34                                                                     (cartprodsndin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairmemEL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairmemER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempaircEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodfstpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodsndpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairsurjEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrSub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setOfPairsIsBReln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrERa) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrEL1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrEL2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcImageSingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (apProp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (app) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (infuncsetfunc) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2p) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcinfuncset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lamProp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lamp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lam2p) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (brelnall1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (brelnall2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1E2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcextLem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subbreln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eqbreln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcext) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcext2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2apEq1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2apEq2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (beta1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eta1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lam2lamEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (beta2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eta2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalseProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalseProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ifSingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ifp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (theeq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrue) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalse) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueorfalse) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setextT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subsetTI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetTI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetTE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectTELcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectTERcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementSub1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementSub2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTnotintersectT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementImpComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contraSubsetComplement) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTcontraSubset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTILcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTIRcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInUnion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTEcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1a) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1b) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2b2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2b) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule0) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_5) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1all2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1SetBreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (choice2fnsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1all1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subbreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eqbreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compEex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionIL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionIR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionEcases) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionCommutes) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2Ex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2W) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2A) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2B) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Ex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Ex1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Equiv) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1E) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1I) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncSetFuncIn) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncSetFuncInj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (leftInvIsSurj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjCantorThm) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (foundation2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (notinself) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (notinself2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (omegaSp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (omegaSclos) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (peano0notS) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (peanoSinj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (transitivesetOp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintTransitive) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (transitivesetOp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionTransitive) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ordinalMinLem1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (!!) @ (
% 122.15/16.35                                                                     ^[Y0 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (ordinal @ 
% 122.15/16.35                                                                      Y0) =>
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (!!) @ (
% 122.15/16.35                                                                      ^[Y1 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (!!) @ (
% 122.15/16.35                                                                      ^[Y2 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y2 @ 
% 122.15/16.35                                                                      Y0) =>
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y1 @ 
% 122.15/16.35                                                                      Y2) =>
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.35      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl746])).
% 122.15/16.35  thf(zip_derived_cl770, plain,
% 122.15/16.35      (~ (((subsetE2) =>
% 122.15/16.35           (((notsubsetI) =>
% 122.15/16.35             (((notequalI1) =>
% 122.15/16.35               (((notequalI2) =>
% 122.15/16.35                 (((subsetRefl) =>
% 122.15/16.35                   (((subsetTrans) =>
% 122.15/16.35                     (((setadjoinSub) =>
% 122.15/16.35                       (((setadjoinSub2) =>
% 122.15/16.35                         (((subset2powerset) =>
% 122.15/16.35                           (((setextsub) =>
% 122.15/16.35                             (((subsetemptysetimpeq) =>
% 122.15/16.35                               (((powersetI1) =>
% 122.15/16.35                                 (((powersetE1) =>
% 122.15/16.35                                   (((inPowerset) =>
% 122.15/16.35                                     (((powersetsubset) =>
% 122.15/16.35                                       (((sepInPowerset) =>
% 122.15/16.35                                         (((sepSubset) =>
% 122.15/16.35                                           (((binunionIL) =>
% 122.15/16.35                                             (((upairset2IR) =>
% 122.15/16.35                                               (((binunionIR) =>
% 122.15/16.35                                                 (((binunionEcases) =>
% 122.15/16.35                                                   (((binunionE) =>
% 122.15/16.35                                                     (((binunionLsub) =>
% 122.15/16.35                                                       (((binunionRsub) =>
% 122.15/16.35                                                         (((binintersectI) =>
% 122.15/16.35                                                           (((binintersectSubset5) =>
% 122.15/16.35                                                             (((binintersectEL) =>
% 122.15/16.35                                                               (((binintersectLsub) =>
% 122.15/16.35                                                                 (((binintersectSubset2) =>
% 122.15/16.35                                                                   (((binintersectSubset3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (disjointsetsI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectRsub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectSubset4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectSubset1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (bs114d) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusEL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusSubset2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusERneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusELneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusILneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusIRneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusLsub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusSubset1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffI2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffIneg1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffIneg2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (secondinupair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairIL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairIR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairiskpair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonsubset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletoninpowerset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletoninpowunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairset2E) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairsubunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairinpowunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempair1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionE2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1E1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1I) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1I2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonsuniq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kfstsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (theprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kfstpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodfstin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR11) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR12) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairequniteq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ksndsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ksndpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairsurjEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodsndin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairmemEL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairmemER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempaircEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodfstpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodsndpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairsurjEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrSub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setOfPairsIsBReln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrERa) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrEL1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrEL2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcImageSingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (apProp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (app) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (infuncsetfunc) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2p) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcinfuncset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lamProp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lamp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lam2p) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (brelnall1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (brelnall2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1E2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcextLem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subbreln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eqbreln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcext) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcext2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2apEq1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2apEq2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (beta1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eta1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lam2lamEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (beta2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eta2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalseProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalseProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ifSingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ifp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (theeq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrue) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalse) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueorfalse) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setextT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subsetTI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetTI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetTE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectTELcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectTERcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementSub1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementSub2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTnotintersectT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementImpComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contraSubsetComplement) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTcontraSubset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTILcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTIRcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInUnion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTEcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1a) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1b) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2b2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2b) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule0) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_5) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1all2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1SetBreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (choice2fnsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1all1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subbreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eqbreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compEex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionIL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionIR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionEcases) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionCommutes) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2Ex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2W) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2A) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2B) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Ex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Ex1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Equiv) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1E) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1I) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncSetFuncIn) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncSetFuncInj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (leftInvIsSurj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjCantorThm) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (foundation2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (notinself) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (notinself2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (omegaSp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (omegaSclos) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (peano0notS) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (peanoSinj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (transitivesetOp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintTransitive) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (transitivesetOp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionTransitive) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ordinalMinLem1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (!!) @ (
% 122.15/16.35                                                                     ^[Y0 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (ordinal @ 
% 122.15/16.35                                                                      Y0) =>
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (!!) @ (
% 122.15/16.35                                                                      ^[Y1 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (!!) @ (
% 122.15/16.35                                                                      ^[Y2 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y2 @ 
% 122.15/16.35                                                                      Y0) =>
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y1 @ 
% 122.15/16.35                                                                      Y2) =>
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.35      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl758])).
% 122.15/16.35  thf(zip_derived_cl783, plain,
% 122.15/16.35      (~ (((notsubsetI) =>
% 122.15/16.35           (((notequalI1) =>
% 122.15/16.35             (((notequalI2) =>
% 122.15/16.35               (((subsetRefl) =>
% 122.15/16.35                 (((subsetTrans) =>
% 122.15/16.35                   (((setadjoinSub) =>
% 122.15/16.35                     (((setadjoinSub2) =>
% 122.15/16.35                       (((subset2powerset) =>
% 122.15/16.35                         (((setextsub) =>
% 122.15/16.35                           (((subsetemptysetimpeq) =>
% 122.15/16.35                             (((powersetI1) =>
% 122.15/16.35                               (((powersetE1) =>
% 122.15/16.35                                 (((inPowerset) =>
% 122.15/16.35                                   (((powersetsubset) =>
% 122.15/16.35                                     (((sepInPowerset) =>
% 122.15/16.35                                       (((sepSubset) =>
% 122.15/16.35                                         (((binunionIL) =>
% 122.15/16.35                                           (((upairset2IR) =>
% 122.15/16.35                                             (((binunionIR) =>
% 122.15/16.35                                               (((binunionEcases) =>
% 122.15/16.35                                                 (((binunionE) =>
% 122.15/16.35                                                   (((binunionLsub) =>
% 122.15/16.35                                                     (((binunionRsub) =>
% 122.15/16.35                                                       (((binintersectI) =>
% 122.15/16.35                                                         (((binintersectSubset5) =>
% 122.15/16.35                                                           (((binintersectEL) =>
% 122.15/16.35                                                             (((binintersectLsub) =>
% 122.15/16.35                                                               (((binintersectSubset2) =>
% 122.15/16.35                                                                 (((binintersectSubset3) =>
% 122.15/16.35                                                                   (((binintersectER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (disjointsetsI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectRsub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectSubset4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectSubset1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (bs114d) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusEL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusSubset2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusERneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusELneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusILneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusIRneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusLsub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusSubset1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffI2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffIneg1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffIneg2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (secondinupair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairIL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairIR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairiskpair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonsubset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletoninpowerset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletoninpowunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairset2E) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairsubunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairinpowunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempair1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionE2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1E1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1I) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1I2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonsuniq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kfstsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (theprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kfstpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodfstin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR11) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR12) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairequniteq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ksndsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ksndpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairsurjEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodsndin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairmemEL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairmemER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempaircEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodfstpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodsndpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairsurjEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrSub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setOfPairsIsBReln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrERa) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrEL1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrEL2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcImageSingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (apProp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (app) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (infuncsetfunc) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2p) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcinfuncset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lamProp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lamp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lam2p) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (brelnall1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (brelnall2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1E2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcextLem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subbreln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eqbreln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcext) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcext2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2apEq1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2apEq2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (beta1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eta1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lam2lamEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (beta2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eta2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalseProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalseProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ifSingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ifp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (theeq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrue) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalse) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueorfalse) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setextT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subsetTI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetTI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetTE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectTELcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectTERcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementSub1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementSub2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTnotintersectT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementImpComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contraSubsetComplement) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTcontraSubset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTILcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTIRcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInUnion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTEcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1a) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1b) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2b2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2b) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule0) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_5) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1all2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1SetBreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (choice2fnsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1all1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subbreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eqbreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compEex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionIL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionIR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionEcases) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionCommutes) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2Ex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2W) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2A) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2B) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Ex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Ex1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Equiv) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1E) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1I) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncSetFuncIn) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncSetFuncInj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (leftInvIsSurj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjCantorThm) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (foundation2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (notinself) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (notinself2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (omegaSp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (omegaSclos) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (peano0notS) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (peanoSinj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (transitivesetOp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintTransitive) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (transitivesetOp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionTransitive) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ordinalMinLem1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (!!) @ (
% 122.15/16.35                                                                     ^[Y0 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (ordinal @ 
% 122.15/16.35                                                                      Y0) =>
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (!!) @ (
% 122.15/16.35                                                                      ^[Y1 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (!!) @ (
% 122.15/16.35                                                                      ^[Y2 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y2 @ 
% 122.15/16.35                                                                      Y0) =>
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y1 @ 
% 122.15/16.35                                                                      Y2) =>
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.35      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl770])).
% 122.15/16.35  thf(zip_derived_cl795, plain,
% 122.15/16.35      (~ (((notequalI1) =>
% 122.15/16.35           (((notequalI2) =>
% 122.15/16.35             (((subsetRefl) =>
% 122.15/16.35               (((subsetTrans) =>
% 122.15/16.35                 (((setadjoinSub) =>
% 122.15/16.35                   (((setadjoinSub2) =>
% 122.15/16.35                     (((subset2powerset) =>
% 122.15/16.35                       (((setextsub) =>
% 122.15/16.35                         (((subsetemptysetimpeq) =>
% 122.15/16.35                           (((powersetI1) =>
% 122.15/16.35                             (((powersetE1) =>
% 122.15/16.35                               (((inPowerset) =>
% 122.15/16.35                                 (((powersetsubset) =>
% 122.15/16.35                                   (((sepInPowerset) =>
% 122.15/16.35                                     (((sepSubset) =>
% 122.15/16.35                                       (((binunionIL) =>
% 122.15/16.35                                         (((upairset2IR) =>
% 122.15/16.35                                           (((binunionIR) =>
% 122.15/16.35                                             (((binunionEcases) =>
% 122.15/16.35                                               (((binunionE) =>
% 122.15/16.35                                                 (((binunionLsub) =>
% 122.15/16.35                                                   (((binunionRsub) =>
% 122.15/16.35                                                     (((binintersectI) =>
% 122.15/16.35                                                       (((binintersectSubset5) =>
% 122.15/16.35                                                         (((binintersectEL) =>
% 122.15/16.35                                                           (((binintersectLsub) =>
% 122.15/16.35                                                             (((binintersectSubset2) =>
% 122.15/16.35                                                               (((binintersectSubset3) =>
% 122.15/16.35                                                                 (((binintersectER) =>
% 122.15/16.35                                                                   (((disjointsetsI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectRsub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectSubset4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectSubset1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (bs114d) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusEL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusSubset2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusERneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusELneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusILneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusIRneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusLsub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusSubset1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffI2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffIneg1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffIneg2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (secondinupair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairIL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairIR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairiskpair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonsubset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletoninpowerset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletoninpowunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairset2E) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairsubunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairinpowunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempair1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionE2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1E1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1I) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1I2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonsuniq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kfstsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (theprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kfstpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodfstin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR11) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR12) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairequniteq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ksndsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ksndpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairsurjEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodsndin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairmemEL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairmemER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempaircEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodfstpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodsndpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairsurjEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrSub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setOfPairsIsBReln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrERa) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrEL1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrEL2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcImageSingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (apProp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (app) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (infuncsetfunc) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2p) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcinfuncset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lamProp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lamp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lam2p) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (brelnall1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (brelnall2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1E2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcextLem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subbreln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eqbreln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcext) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcext2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2apEq1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2apEq2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (beta1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eta1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lam2lamEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (beta2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eta2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalseProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalseProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ifSingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ifp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (theeq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrue) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalse) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueorfalse) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setextT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subsetTI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetTI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetTE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectTELcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectTERcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementSub1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementSub2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTnotintersectT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementImpComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contraSubsetComplement) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTcontraSubset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTILcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTIRcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInUnion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTEcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1a) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1b) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2b2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2b) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule0) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_5) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1all2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1SetBreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (choice2fnsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1all1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subbreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eqbreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compEex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionIL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionIR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionEcases) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionCommutes) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2Ex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2W) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2A) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2B) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Ex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Ex1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Equiv) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1E) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1I) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncSetFuncIn) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncSetFuncInj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (leftInvIsSurj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjCantorThm) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (foundation2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (notinself) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (notinself2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (omegaSp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (omegaSclos) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (peano0notS) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (peanoSinj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (transitivesetOp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintTransitive) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (transitivesetOp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionTransitive) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ordinalMinLem1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (!!) @ (
% 122.15/16.35                                                                     ^[Y0 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (ordinal @ 
% 122.15/16.35                                                                      Y0) =>
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (!!) @ (
% 122.15/16.35                                                                      ^[Y1 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (!!) @ (
% 122.15/16.35                                                                      ^[Y2 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y2 @ 
% 122.15/16.35                                                                      Y0) =>
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y1 @ 
% 122.15/16.35                                                                      Y2) =>
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.35      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl783])).
% 122.15/16.35  thf(zip_derived_cl805, plain,
% 122.15/16.35      (~ (((notequalI2) =>
% 122.15/16.35           (((subsetRefl) =>
% 122.15/16.35             (((subsetTrans) =>
% 122.15/16.35               (((setadjoinSub) =>
% 122.15/16.35                 (((setadjoinSub2) =>
% 122.15/16.35                   (((subset2powerset) =>
% 122.15/16.35                     (((setextsub) =>
% 122.15/16.35                       (((subsetemptysetimpeq) =>
% 122.15/16.35                         (((powersetI1) =>
% 122.15/16.35                           (((powersetE1) =>
% 122.15/16.35                             (((inPowerset) =>
% 122.15/16.35                               (((powersetsubset) =>
% 122.15/16.35                                 (((sepInPowerset) =>
% 122.15/16.35                                   (((sepSubset) =>
% 122.15/16.35                                     (((binunionIL) =>
% 122.15/16.35                                       (((upairset2IR) =>
% 122.15/16.35                                         (((binunionIR) =>
% 122.15/16.35                                           (((binunionEcases) =>
% 122.15/16.35                                             (((binunionE) =>
% 122.15/16.35                                               (((binunionLsub) =>
% 122.15/16.35                                                 (((binunionRsub) =>
% 122.15/16.35                                                   (((binintersectI) =>
% 122.15/16.35                                                     (((binintersectSubset5) =>
% 122.15/16.35                                                       (((binintersectEL) =>
% 122.15/16.35                                                         (((binintersectLsub) =>
% 122.15/16.35                                                           (((binintersectSubset2) =>
% 122.15/16.35                                                             (((binintersectSubset3) =>
% 122.15/16.35                                                               (((binintersectER) =>
% 122.15/16.35                                                                 (((disjointsetsI1) =>
% 122.15/16.35                                                                   (((binintersectRsub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectSubset4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectSubset1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (bs114d) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusEL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusSubset2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusERneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusELneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusILneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusIRneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusLsub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusSubset1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffI2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffIneg1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffIneg2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (secondinupair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairIL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairIR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairiskpair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonsubset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletoninpowerset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletoninpowunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairset2E) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairsubunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairinpowunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempair1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionE2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1E1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1I) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1I2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonsuniq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kfstsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (theprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kfstpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodfstin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR11) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR12) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairequniteq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ksndsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ksndpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairsurjEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodsndin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairmemEL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairmemER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempaircEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodfstpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodsndpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairsurjEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrSub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setOfPairsIsBReln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrERa) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrEL1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrEL2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcImageSingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (apProp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (app) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (infuncsetfunc) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2p) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcinfuncset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lamProp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lamp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lam2p) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (brelnall1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (brelnall2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1E2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcextLem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subbreln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eqbreln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcext) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcext2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2apEq1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2apEq2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (beta1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eta1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lam2lamEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (beta2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eta2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalseProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalseProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ifSingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ifp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (theeq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrue) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalse) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueorfalse) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setextT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subsetTI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetTI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetTE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectTELcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectTERcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contrasubsetT3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementE1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementSub1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementSub2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (doubleComplementEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTnotintersectT) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementImpComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementSubsetComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementInPowersetComplementIntersect) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (contraSubsetComplement) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementTcontraSubset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTILcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTIRcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInUnion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInUnion2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inIntersectImpInIntersectUnions) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (intersectInPowersetIntersectUnions) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inComplementUnionImpNotIn1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (inComplementUnionImpInComplement1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionTEcontra) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (complementUnionInPowersetComplement) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1a) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1b) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2a) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2b2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2b) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (demorgan2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule0) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz13rule4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz1_5) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1all2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1SetBreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (choice2fnsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setOfPairsIsBReln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1all1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subbreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eqbreln1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1invE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1compEex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionIL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionIR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionEcases) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (breln1unionCommutes) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2Ex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2W) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2A) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (woz2B) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Ex) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Ex1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1Equiv) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1E) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (image1I) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncInInjFuncSet) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncSetFuncIn) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (injFuncSetFuncInj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjFuncSetFuncIn) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjFuncSetFuncSurj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (leftInvIsSurj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (surjCantorThm) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (foundation2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (notinself) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (notinself2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (omegaSp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (omegaSclos) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (peano0notS) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (peanoSinj) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (transitivesetOp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintTransitive) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (transitivesetOp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionTransitive) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ordinalMinLem1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (!!) @ (
% 122.15/16.35                                                                     ^[Y0 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (ordinal @ 
% 122.15/16.35                                                                      Y0) =>
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (!!) @ (
% 122.15/16.35                                                                      ^[Y1 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (!!) @ (
% 122.15/16.35                                                                      ^[Y2 : $i]:
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y2 @ 
% 122.15/16.35                                                                      Y0) =>
% 122.15/16.35                                                                      ((
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y1 @ 
% 122.15/16.35                                                                      Y2) =>
% 122.15/16.35                                                                      (in @ 
% 122.15/16.35                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.15/16.35      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl795])).
% 122.15/16.35  thf(zip_derived_cl813, plain,
% 122.15/16.35      (~ (((subsetRefl) =>
% 122.15/16.35           (((subsetTrans) =>
% 122.15/16.35             (((setadjoinSub) =>
% 122.15/16.35               (((setadjoinSub2) =>
% 122.15/16.35                 (((subset2powerset) =>
% 122.15/16.35                   (((setextsub) =>
% 122.15/16.35                     (((subsetemptysetimpeq) =>
% 122.15/16.35                       (((powersetI1) =>
% 122.15/16.35                         (((powersetE1) =>
% 122.15/16.35                           (((inPowerset) =>
% 122.15/16.35                             (((powersetsubset) =>
% 122.15/16.35                               (((sepInPowerset) =>
% 122.15/16.35                                 (((sepSubset) =>
% 122.15/16.35                                   (((binunionIL) =>
% 122.15/16.35                                     (((upairset2IR) =>
% 122.15/16.35                                       (((binunionIR) =>
% 122.15/16.35                                         (((binunionEcases) =>
% 122.15/16.35                                           (((binunionE) =>
% 122.15/16.35                                             (((binunionLsub) =>
% 122.15/16.35                                               (((binunionRsub) =>
% 122.15/16.35                                                 (((binintersectI) =>
% 122.15/16.35                                                   (((binintersectSubset5) =>
% 122.15/16.35                                                     (((binintersectEL) =>
% 122.15/16.35                                                       (((binintersectLsub) =>
% 122.15/16.35                                                         (((binintersectSubset2) =>
% 122.15/16.35                                                           (((binintersectSubset3) =>
% 122.15/16.35                                                             (((binintersectER) =>
% 122.15/16.35                                                               (((disjointsetsI1) =>
% 122.15/16.35                                                                 (((binintersectRsub) =>
% 122.15/16.35                                                                   (((binintersectSubset4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectSubset1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (bs114d) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusEL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusSubset2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusERneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusELneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusILneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusIRneg) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusLsub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setminusSubset1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffE) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffI1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffI2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffIneg1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (symdiffIneg2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (secondinupair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairIL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairIR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairiskpair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonsubset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletoninpowerset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletoninpowunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairset2E) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairsubunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairinpowunion) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ubforcartprodlem3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempair1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempair) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionE2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setunionsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1E1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1I) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1I2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (singletonsuniq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kfstsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (theprop) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kfstpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodfstin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR11) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR12) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (upairequniteq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setukpairinjR) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ksndsingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ksndpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (kpairsurjEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodsndin) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairmemEL) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairmemER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodmempaircEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodfstpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodsndpairEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (cartprodpairsurjEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrI) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrSub) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (setOfPairsIsBReln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrERa) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrEL1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrEL2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (dpsetconstrER) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcImageSingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (apProp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (app) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (infuncsetfunc) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2p) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcinfuncset) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lamProp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lamp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lam2p) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (brelnall1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (brelnall2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ex1E2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp3) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcextLem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcGraphProp4) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (subbreln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eqbreln) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcext) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (funcext2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2apEq1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ap2apEq2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (beta1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eta1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (lam2lamEq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (beta2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (eta2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalseProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalseProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueProp1) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueProp2) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ifSingleton) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (ifp) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (theeq) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrue) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iffalse) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (iftrueorfalse) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binintersectT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (binunionT_lem) =>
% 122.15/16.35                                                                     ((
% 122.15/16.35                                                                     (powersetT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setextT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subsetTI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetTI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetTE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectTELcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectTERcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementSub1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementSub2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTnotintersectT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementImpComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contraSubsetComplement) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTcontraSubset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTILcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTIRcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInUnion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTEcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1a) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1b) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2b2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2b) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule0) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_5) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1all2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1SetBreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (choice2fnsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1all1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subbreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eqbreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compEex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionIL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionIR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionEcases) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionCommutes) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2Ex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2W) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2A) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2B) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Ex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Ex1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Equiv) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1E) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1I) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncSetFuncIn) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncSetFuncInj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (leftInvIsSurj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjCantorThm) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (foundation2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (notinself) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (notinself2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (omegaSp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (omegaSclos) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (peano0notS) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (peanoSinj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (transitivesetOp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintTransitive) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (transitivesetOp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionTransitive) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ordinalMinLem1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (!!) @ (
% 122.49/16.35                                                                     ^[Y0 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (ordinal @ 
% 122.49/16.35                                                                      Y0) =>
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (!!) @ (
% 122.49/16.35                                                                      ^[Y1 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (!!) @ (
% 122.49/16.35                                                                      ^[Y2 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y2 @ 
% 122.49/16.35                                                                      Y0) =>
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y1 @ 
% 122.49/16.35                                                                      Y2) =>
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.35      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl805])).
% 122.49/16.35  thf(zip_derived_cl823, plain,
% 122.49/16.35      (~ (((subsetTrans) =>
% 122.49/16.35           (((setadjoinSub) =>
% 122.49/16.35             (((setadjoinSub2) =>
% 122.49/16.35               (((subset2powerset) =>
% 122.49/16.35                 (((setextsub) =>
% 122.49/16.35                   (((subsetemptysetimpeq) =>
% 122.49/16.35                     (((powersetI1) =>
% 122.49/16.35                       (((powersetE1) =>
% 122.49/16.35                         (((inPowerset) =>
% 122.49/16.35                           (((powersetsubset) =>
% 122.49/16.35                             (((sepInPowerset) =>
% 122.49/16.35                               (((sepSubset) =>
% 122.49/16.35                                 (((binunionIL) =>
% 122.49/16.35                                   (((upairset2IR) =>
% 122.49/16.35                                     (((binunionIR) =>
% 122.49/16.35                                       (((binunionEcases) =>
% 122.49/16.35                                         (((binunionE) =>
% 122.49/16.35                                           (((binunionLsub) =>
% 122.49/16.35                                             (((binunionRsub) =>
% 122.49/16.35                                               (((binintersectI) =>
% 122.49/16.35                                                 (((binintersectSubset5) =>
% 122.49/16.35                                                   (((binintersectEL) =>
% 122.49/16.35                                                     (((binintersectLsub) =>
% 122.49/16.35                                                       (((binintersectSubset2) =>
% 122.49/16.35                                                         (((binintersectSubset3) =>
% 122.49/16.35                                                           (((binintersectER) =>
% 122.49/16.35                                                             (((disjointsetsI1) =>
% 122.49/16.35                                                               (((binintersectRsub) =>
% 122.49/16.35                                                                 (((binintersectSubset4) =>
% 122.49/16.35                                                                   (((binintersectSubset1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (bs114d) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusEL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusSubset2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusERneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusELneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusILneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusIRneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusLsub) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusSubset1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffI2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffIneg1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffIneg2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (secondinupair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairIL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairIR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairiskpair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonsubset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletoninpowerset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletoninpowunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairset2E) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairsubunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairinpowunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempair1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionE2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1E1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1I) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1I2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonsuniq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kfstsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (theprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kfstpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodfstin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR11) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR12) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairequniteq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ksndsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ksndpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairsurjEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodsndin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairmemEL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairmemER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempaircEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodfstpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodsndpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairsurjEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrSub) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setOfPairsIsBReln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrERa) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrEL1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrEL2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcImageSingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (apProp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (app) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (infuncsetfunc) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2p) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcinfuncset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lamProp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lamp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lam2p) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (brelnall1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (brelnall2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1E2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcextLem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subbreln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eqbreln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcext) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcext2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2apEq1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2apEq2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (beta1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eta1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lam2lamEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (beta2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eta2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalseProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalseProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ifSingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ifp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (theeq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrue) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalse) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueorfalse) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setextT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subsetTI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetTI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetTE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectTELcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectTERcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementSub1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementSub2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTnotintersectT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementImpComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contraSubsetComplement) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTcontraSubset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTILcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTIRcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInUnion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTEcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1a) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1b) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2b2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2b) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule0) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_5) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1all2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1SetBreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (choice2fnsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1all1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subbreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eqbreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compEex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionIL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionIR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionEcases) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionCommutes) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2Ex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2W) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2A) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2B) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Ex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Ex1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Equiv) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1E) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1I) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncSetFuncIn) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncSetFuncInj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (leftInvIsSurj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjCantorThm) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (foundation2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (notinself) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (notinself2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (omegaSp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (omegaSclos) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (peano0notS) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (peanoSinj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (transitivesetOp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintTransitive) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (transitivesetOp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionTransitive) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ordinalMinLem1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (!!) @ (
% 122.49/16.35                                                                     ^[Y0 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (ordinal @ 
% 122.49/16.35                                                                      Y0) =>
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (!!) @ (
% 122.49/16.35                                                                      ^[Y1 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (!!) @ (
% 122.49/16.35                                                                      ^[Y2 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y2 @ 
% 122.49/16.35                                                                      Y0) =>
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y1 @ 
% 122.49/16.35                                                                      Y2) =>
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.35      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl813])).
% 122.49/16.35  thf(zip_derived_cl833, plain,
% 122.49/16.35      (~ (((setadjoinSub) =>
% 122.49/16.35           (((setadjoinSub2) =>
% 122.49/16.35             (((subset2powerset) =>
% 122.49/16.35               (((setextsub) =>
% 122.49/16.35                 (((subsetemptysetimpeq) =>
% 122.49/16.35                   (((powersetI1) =>
% 122.49/16.35                     (((powersetE1) =>
% 122.49/16.35                       (((inPowerset) =>
% 122.49/16.35                         (((powersetsubset) =>
% 122.49/16.35                           (((sepInPowerset) =>
% 122.49/16.35                             (((sepSubset) =>
% 122.49/16.35                               (((binunionIL) =>
% 122.49/16.35                                 (((upairset2IR) =>
% 122.49/16.35                                   (((binunionIR) =>
% 122.49/16.35                                     (((binunionEcases) =>
% 122.49/16.35                                       (((binunionE) =>
% 122.49/16.35                                         (((binunionLsub) =>
% 122.49/16.35                                           (((binunionRsub) =>
% 122.49/16.35                                             (((binintersectI) =>
% 122.49/16.35                                               (((binintersectSubset5) =>
% 122.49/16.35                                                 (((binintersectEL) =>
% 122.49/16.35                                                   (((binintersectLsub) =>
% 122.49/16.35                                                     (((binintersectSubset2) =>
% 122.49/16.35                                                       (((binintersectSubset3) =>
% 122.49/16.35                                                         (((binintersectER) =>
% 122.49/16.35                                                           (((disjointsetsI1) =>
% 122.49/16.35                                                             (((binintersectRsub) =>
% 122.49/16.35                                                               (((binintersectSubset4) =>
% 122.49/16.35                                                                 (((binintersectSubset1) =>
% 122.49/16.35                                                                   (((bs114d) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusEL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusSubset2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusERneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusELneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusILneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusIRneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusLsub) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusSubset1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffI2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffIneg1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffIneg2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (secondinupair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairIL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairIR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairiskpair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonsubset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletoninpowerset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletoninpowunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairset2E) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairsubunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairinpowunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempair1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionE2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1E1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1I) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1I2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonsuniq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kfstsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (theprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kfstpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodfstin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR11) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR12) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairequniteq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ksndsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ksndpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairsurjEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodsndin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairmemEL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairmemER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempaircEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodfstpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodsndpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairsurjEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrSub) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setOfPairsIsBReln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrERa) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrEL1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrEL2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcImageSingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (apProp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (app) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (infuncsetfunc) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2p) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcinfuncset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lamProp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lamp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lam2p) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (brelnall1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (brelnall2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1E2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcextLem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subbreln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eqbreln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcext) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcext2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2apEq1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2apEq2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (beta1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eta1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lam2lamEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (beta2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eta2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalseProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalseProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ifSingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ifp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (theeq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrue) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalse) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueorfalse) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setextT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subsetTI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetTI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetTE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectTELcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectTERcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementSub1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementSub2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTnotintersectT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementImpComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contraSubsetComplement) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTcontraSubset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTILcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTIRcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInUnion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTEcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1a) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1b) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2b2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2b) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule0) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_5) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1all2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1SetBreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (choice2fnsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1all1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subbreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eqbreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compEex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionIL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionIR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionEcases) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionCommutes) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2Ex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2W) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2A) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2B) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Ex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Ex1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Equiv) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1E) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1I) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncSetFuncIn) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncSetFuncInj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (leftInvIsSurj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjCantorThm) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (foundation2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (notinself) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (notinself2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (omegaSp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (omegaSclos) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (peano0notS) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (peanoSinj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (transitivesetOp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintTransitive) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (transitivesetOp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionTransitive) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ordinalMinLem1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (!!) @ (
% 122.49/16.35                                                                     ^[Y0 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (ordinal @ 
% 122.49/16.35                                                                      Y0) =>
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (!!) @ (
% 122.49/16.35                                                                      ^[Y1 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (!!) @ (
% 122.49/16.35                                                                      ^[Y2 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y2 @ 
% 122.49/16.35                                                                      Y0) =>
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y1 @ 
% 122.49/16.35                                                                      Y2) =>
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.35      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl823])).
% 122.49/16.35  thf(zip_derived_cl843, plain,
% 122.49/16.35      (~ (((setadjoinSub2) =>
% 122.49/16.35           (((subset2powerset) =>
% 122.49/16.35             (((setextsub) =>
% 122.49/16.35               (((subsetemptysetimpeq) =>
% 122.49/16.35                 (((powersetI1) =>
% 122.49/16.35                   (((powersetE1) =>
% 122.49/16.35                     (((inPowerset) =>
% 122.49/16.35                       (((powersetsubset) =>
% 122.49/16.35                         (((sepInPowerset) =>
% 122.49/16.35                           (((sepSubset) =>
% 122.49/16.35                             (((binunionIL) =>
% 122.49/16.35                               (((upairset2IR) =>
% 122.49/16.35                                 (((binunionIR) =>
% 122.49/16.35                                   (((binunionEcases) =>
% 122.49/16.35                                     (((binunionE) =>
% 122.49/16.35                                       (((binunionLsub) =>
% 122.49/16.35                                         (((binunionRsub) =>
% 122.49/16.35                                           (((binintersectI) =>
% 122.49/16.35                                             (((binintersectSubset5) =>
% 122.49/16.35                                               (((binintersectEL) =>
% 122.49/16.35                                                 (((binintersectLsub) =>
% 122.49/16.35                                                   (((binintersectSubset2) =>
% 122.49/16.35                                                     (((binintersectSubset3) =>
% 122.49/16.35                                                       (((binintersectER) =>
% 122.49/16.35                                                         (((disjointsetsI1) =>
% 122.49/16.35                                                           (((binintersectRsub) =>
% 122.49/16.35                                                             (((binintersectSubset4) =>
% 122.49/16.35                                                               (((binintersectSubset1) =>
% 122.49/16.35                                                                 (((bs114d) =>
% 122.49/16.35                                                                   (((setminusI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusEL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusSubset2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusERneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusELneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusILneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusIRneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusLsub) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusSubset1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffI2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffIneg1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffIneg2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (secondinupair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairIL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairIR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairiskpair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonsubset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletoninpowerset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletoninpowunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairset2E) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairsubunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairinpowunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempair1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionE2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1E1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1I) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1I2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonsuniq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kfstsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (theprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kfstpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodfstin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR11) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR12) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairequniteq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ksndsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ksndpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairsurjEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodsndin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairmemEL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairmemER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempaircEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodfstpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodsndpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairsurjEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrSub) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setOfPairsIsBReln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrERa) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrEL1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrEL2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcImageSingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (apProp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (app) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (infuncsetfunc) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2p) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcinfuncset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lamProp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lamp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lam2p) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (brelnall1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (brelnall2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1E2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcextLem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subbreln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eqbreln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcext) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcext2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2apEq1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2apEq2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (beta1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eta1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lam2lamEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (beta2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eta2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalseProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalseProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ifSingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ifp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (theeq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrue) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalse) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueorfalse) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setextT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subsetTI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetTI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetTE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectTELcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectTERcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementSub1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementSub2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTnotintersectT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementImpComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contraSubsetComplement) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTcontraSubset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTILcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTIRcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInUnion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTEcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1a) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1b) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2b2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2b) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule0) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_5) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1all2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1SetBreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (choice2fnsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1all1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subbreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eqbreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compEex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionIL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionIR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionEcases) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionCommutes) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2Ex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2W) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2A) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2B) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Ex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Ex1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Equiv) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1E) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1I) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncSetFuncIn) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncSetFuncInj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (leftInvIsSurj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjCantorThm) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (foundation2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (notinself) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (notinself2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (omegaSp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (omegaSclos) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (peano0notS) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (peanoSinj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (transitivesetOp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintTransitive) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (transitivesetOp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionTransitive) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ordinalMinLem1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (!!) @ (
% 122.49/16.35                                                                     ^[Y0 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (ordinal @ 
% 122.49/16.35                                                                      Y0) =>
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (!!) @ (
% 122.49/16.35                                                                      ^[Y1 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (!!) @ (
% 122.49/16.35                                                                      ^[Y2 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y2 @ 
% 122.49/16.35                                                                      Y0) =>
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y1 @ 
% 122.49/16.35                                                                      Y2) =>
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.35      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl833])).
% 122.49/16.35  thf(zip_derived_cl851, plain,
% 122.49/16.35      (~ (((subset2powerset) =>
% 122.49/16.35           (((setextsub) =>
% 122.49/16.35             (((subsetemptysetimpeq) =>
% 122.49/16.35               (((powersetI1) =>
% 122.49/16.35                 (((powersetE1) =>
% 122.49/16.35                   (((inPowerset) =>
% 122.49/16.35                     (((powersetsubset) =>
% 122.49/16.35                       (((sepInPowerset) =>
% 122.49/16.35                         (((sepSubset) =>
% 122.49/16.35                           (((binunionIL) =>
% 122.49/16.35                             (((upairset2IR) =>
% 122.49/16.35                               (((binunionIR) =>
% 122.49/16.35                                 (((binunionEcases) =>
% 122.49/16.35                                   (((binunionE) =>
% 122.49/16.35                                     (((binunionLsub) =>
% 122.49/16.35                                       (((binunionRsub) =>
% 122.49/16.35                                         (((binintersectI) =>
% 122.49/16.35                                           (((binintersectSubset5) =>
% 122.49/16.35                                             (((binintersectEL) =>
% 122.49/16.35                                               (((binintersectLsub) =>
% 122.49/16.35                                                 (((binintersectSubset2) =>
% 122.49/16.35                                                   (((binintersectSubset3) =>
% 122.49/16.35                                                     (((binintersectER) =>
% 122.49/16.35                                                       (((disjointsetsI1) =>
% 122.49/16.35                                                         (((binintersectRsub) =>
% 122.49/16.35                                                           (((binintersectSubset4) =>
% 122.49/16.35                                                             (((binintersectSubset1) =>
% 122.49/16.35                                                               (((bs114d) =>
% 122.49/16.35                                                                 (((setminusI) =>
% 122.49/16.35                                                                   (((setminusEL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusSubset2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusERneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusELneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusILneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusIRneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusLsub) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusSubset1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffI2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffIneg1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffIneg2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (secondinupair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairIL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairIR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairiskpair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonsubset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletoninpowerset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletoninpowunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairset2E) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairsubunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairinpowunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempair1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionE2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1E1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1I) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1I2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonsuniq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kfstsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (theprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kfstpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodfstin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR11) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR12) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairequniteq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ksndsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ksndpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairsurjEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodsndin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairmemEL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairmemER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempaircEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodfstpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodsndpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairsurjEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrSub) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setOfPairsIsBReln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrERa) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrEL1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrEL2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcImageSingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (apProp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (app) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (infuncsetfunc) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2p) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcinfuncset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lamProp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lamp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lam2p) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (brelnall1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (brelnall2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1E2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcextLem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subbreln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eqbreln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcext) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcext2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2apEq1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2apEq2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (beta1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eta1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lam2lamEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (beta2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eta2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalseProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalseProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ifSingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ifp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (theeq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrue) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalse) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueorfalse) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setextT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subsetTI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetTI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetTE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectTELcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectTERcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementSub1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementSub2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTnotintersectT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementImpComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contraSubsetComplement) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTcontraSubset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTILcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTIRcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInUnion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTEcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1a) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1b) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2b2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2b) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule0) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_5) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1all2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1SetBreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (choice2fnsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1all1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subbreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eqbreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compEex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionIL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionIR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionEcases) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionCommutes) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2Ex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2W) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2A) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2B) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Ex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Ex1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Equiv) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1E) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1I) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncSetFuncIn) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncSetFuncInj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (leftInvIsSurj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjCantorThm) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (foundation2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (notinself) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (notinself2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (omegaSp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (omegaSclos) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (peano0notS) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (peanoSinj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (transitivesetOp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintTransitive) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (transitivesetOp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionTransitive) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ordinalMinLem1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (!!) @ (
% 122.49/16.35                                                                     ^[Y0 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (ordinal @ 
% 122.49/16.35                                                                      Y0) =>
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (!!) @ (
% 122.49/16.35                                                                      ^[Y1 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (!!) @ (
% 122.49/16.35                                                                      ^[Y2 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y2 @ 
% 122.49/16.35                                                                      Y0) =>
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y1 @ 
% 122.49/16.35                                                                      Y2) =>
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.35      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl843])).
% 122.49/16.35  thf(zip_derived_cl857, plain,
% 122.49/16.35      (~ (((setextsub) =>
% 122.49/16.35           (((subsetemptysetimpeq) =>
% 122.49/16.35             (((powersetI1) =>
% 122.49/16.35               (((powersetE1) =>
% 122.49/16.35                 (((inPowerset) =>
% 122.49/16.35                   (((powersetsubset) =>
% 122.49/16.35                     (((sepInPowerset) =>
% 122.49/16.35                       (((sepSubset) =>
% 122.49/16.35                         (((binunionIL) =>
% 122.49/16.35                           (((upairset2IR) =>
% 122.49/16.35                             (((binunionIR) =>
% 122.49/16.35                               (((binunionEcases) =>
% 122.49/16.35                                 (((binunionE) =>
% 122.49/16.35                                   (((binunionLsub) =>
% 122.49/16.35                                     (((binunionRsub) =>
% 122.49/16.35                                       (((binintersectI) =>
% 122.49/16.35                                         (((binintersectSubset5) =>
% 122.49/16.35                                           (((binintersectEL) =>
% 122.49/16.35                                             (((binintersectLsub) =>
% 122.49/16.35                                               (((binintersectSubset2) =>
% 122.49/16.35                                                 (((binintersectSubset3) =>
% 122.49/16.35                                                   (((binintersectER) =>
% 122.49/16.35                                                     (((disjointsetsI1) =>
% 122.49/16.35                                                       (((binintersectRsub) =>
% 122.49/16.35                                                         (((binintersectSubset4) =>
% 122.49/16.35                                                           (((binintersectSubset1) =>
% 122.49/16.35                                                             (((bs114d) =>
% 122.49/16.35                                                               (((setminusI) =>
% 122.49/16.35                                                                 (((setminusEL) =>
% 122.49/16.35                                                                   (((setminusER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusSubset2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusERneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusELneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusILneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusIRneg) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusLsub) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusSubset1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffI2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffIneg1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (symdiffIneg2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (secondinupair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairIL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairIR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairiskpair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonsubset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletoninpowerset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletoninpowunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairset2E) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairsubunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairinpowunion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ubforcartprodlem3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempair1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempair) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionE2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1E1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1I) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1I2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (singletonsuniq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kfstsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (theprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kfstpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodfstin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR11) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR12) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (upairequniteq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setukpairinjR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ksndsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ksndpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (kpairsurjEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodsndin) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairmemEL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairmemER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodmempaircEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodfstpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodsndpairEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (cartprodpairsurjEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrSub) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setOfPairsIsBReln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrERa) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrEL1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrEL2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (dpsetconstrER) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcImageSingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (apProp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (app) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (infuncsetfunc) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2p) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcinfuncset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lamProp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lamp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lam2p) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (brelnall1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (brelnall2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ex1E2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcextLem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcGraphProp4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subbreln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eqbreln) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcext) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (funcext2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2apEq1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ap2apEq2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (beta1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eta1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (lam2lamEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (beta2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eta2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalseProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalseProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueProp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueProp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ifSingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ifp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (theeq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrue) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iffalse) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (iftrueorfalse) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setminusT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementT_lem) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setextT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subsetTI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetTI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (powersetTE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectTELcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintersectTERcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contrasubsetT3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementI1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementE1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementSub1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementSub2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (doubleComplementEq) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTnotintersectT) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementImpComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (contraSubsetComplement) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementTcontraSubset) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTILcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTIRcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInUnion) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binunionTEcontra) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1a) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1b) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2a) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2b2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2b) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (demorgan2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule0) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz13rule4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_3) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_4) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz1_5) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1all2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1SetBreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (choice2fnsingleton) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1all1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (subbreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (eqbreln1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1invE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1compEex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionprop) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionIL) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionIR) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionI) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionE) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionEcases) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (breln1unionCommutes) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2Ex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2W) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2A) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (woz2B) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Ex) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Ex1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1Equiv) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1E) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (image1I) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncSetFuncIn) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (injFuncSetFuncInj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (leftInvIsSurj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (surjCantorThm) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (foundation2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (notinself) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (notinself2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (omegaSp) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (omegaSclos) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (peano0notS) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (peanoSinj) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (transitivesetOp1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (binintTransitive) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (transitivesetOp2) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (setunionTransitive) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (ordinalMinLem1) =>
% 122.49/16.35                                                                     ((
% 122.49/16.35                                                                     (!!) @ (
% 122.49/16.35                                                                     ^[Y0 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (ordinal @ 
% 122.49/16.35                                                                      Y0) =>
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (!!) @ (
% 122.49/16.35                                                                      ^[Y1 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (!!) @ (
% 122.49/16.35                                                                      ^[Y2 : $i]:
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y2 @ 
% 122.49/16.35                                                                      Y0) =>
% 122.49/16.35                                                                      ((
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y1 @ 
% 122.49/16.35                                                                      Y2) =>
% 122.49/16.35                                                                      (in @ 
% 122.49/16.35                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.36      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl851])).
% 122.49/16.36  thf(zip_derived_cl864, plain,
% 122.49/16.36      (~ (((subsetemptysetimpeq) =>
% 122.49/16.36           (((powersetI1) =>
% 122.49/16.36             (((powersetE1) =>
% 122.49/16.36               (((inPowerset) =>
% 122.49/16.36                 (((powersetsubset) =>
% 122.49/16.36                   (((sepInPowerset) =>
% 122.49/16.36                     (((sepSubset) =>
% 122.49/16.36                       (((binunionIL) =>
% 122.49/16.36                         (((upairset2IR) =>
% 122.49/16.36                           (((binunionIR) =>
% 122.49/16.36                             (((binunionEcases) =>
% 122.49/16.36                               (((binunionE) =>
% 122.49/16.36                                 (((binunionLsub) =>
% 122.49/16.36                                   (((binunionRsub) =>
% 122.49/16.36                                     (((binintersectI) =>
% 122.49/16.36                                       (((binintersectSubset5) =>
% 122.49/16.36                                         (((binintersectEL) =>
% 122.49/16.36                                           (((binintersectLsub) =>
% 122.49/16.36                                             (((binintersectSubset2) =>
% 122.49/16.36                                               (((binintersectSubset3) =>
% 122.49/16.36                                                 (((binintersectER) =>
% 122.49/16.36                                                   (((disjointsetsI1) =>
% 122.49/16.36                                                     (((binintersectRsub) =>
% 122.49/16.36                                                       (((binintersectSubset4) =>
% 122.49/16.36                                                         (((binintersectSubset1) =>
% 122.49/16.36                                                           (((bs114d) =>
% 122.49/16.36                                                             (((setminusI) =>
% 122.49/16.36                                                               (((setminusEL) =>
% 122.49/16.36                                                                 (((setminusER) =>
% 122.49/16.36                                                                   (((setminusSubset2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusERneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusELneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusILneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusIRneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusLsub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusSubset1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (secondinupair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairiskpair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowerset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairset2E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairsubunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairinpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionE2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsuniq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR11) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR12) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairequniteq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemEL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempaircEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrSub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrERa) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcImageSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (apProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (app) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (infuncsetfunc) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcinfuncset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcextLem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2lamEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theeq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrue) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueorfalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setextT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subsetTI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTELcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTERcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTnotintersectT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementImpComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contraSubsetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTcontraSubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTILcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTIRcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTEcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule0) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_5) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1SetBreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (choice2fnsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compEex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionEcases) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionCommutes) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2W) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2A) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2B) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Equiv) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncInj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (leftInvIsSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjCantorThm) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (foundation2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSclos) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peano0notS) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peanoSinj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ordinalMinLem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (!!) @ (
% 122.49/16.36                                                                     ^[Y0 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (ordinal @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y1 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y2 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y2 @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ 
% 122.49/16.36                                                                      Y2) =>
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.36      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl857])).
% 122.49/16.36  thf(zip_derived_cl872, plain,
% 122.49/16.36      (~ (((powersetI1) =>
% 122.49/16.36           (((powersetE1) =>
% 122.49/16.36             (((inPowerset) =>
% 122.49/16.36               (((powersetsubset) =>
% 122.49/16.36                 (((sepInPowerset) =>
% 122.49/16.36                   (((sepSubset) =>
% 122.49/16.36                     (((binunionIL) =>
% 122.49/16.36                       (((upairset2IR) =>
% 122.49/16.36                         (((binunionIR) =>
% 122.49/16.36                           (((binunionEcases) =>
% 122.49/16.36                             (((binunionE) =>
% 122.49/16.36                               (((binunionLsub) =>
% 122.49/16.36                                 (((binunionRsub) =>
% 122.49/16.36                                   (((binintersectI) =>
% 122.49/16.36                                     (((binintersectSubset5) =>
% 122.49/16.36                                       (((binintersectEL) =>
% 122.49/16.36                                         (((binintersectLsub) =>
% 122.49/16.36                                           (((binintersectSubset2) =>
% 122.49/16.36                                             (((binintersectSubset3) =>
% 122.49/16.36                                               (((binintersectER) =>
% 122.49/16.36                                                 (((disjointsetsI1) =>
% 122.49/16.36                                                   (((binintersectRsub) =>
% 122.49/16.36                                                     (((binintersectSubset4) =>
% 122.49/16.36                                                       (((binintersectSubset1) =>
% 122.49/16.36                                                         (((bs114d) =>
% 122.49/16.36                                                           (((setminusI) =>
% 122.49/16.36                                                             (((setminusEL) =>
% 122.49/16.36                                                               (((setminusER) =>
% 122.49/16.36                                                                 (((setminusSubset2) =>
% 122.49/16.36                                                                   (((setminusERneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusELneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusILneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusIRneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusLsub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusSubset1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (secondinupair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairiskpair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowerset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairset2E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairsubunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairinpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionE2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsuniq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR11) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR12) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairequniteq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemEL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempaircEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrSub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrERa) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcImageSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (apProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (app) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (infuncsetfunc) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcinfuncset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcextLem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2lamEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theeq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrue) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueorfalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setextT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subsetTI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTELcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTERcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTnotintersectT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementImpComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contraSubsetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTcontraSubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTILcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTIRcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTEcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule0) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_5) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1SetBreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (choice2fnsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compEex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionEcases) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionCommutes) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2W) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2A) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2B) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Equiv) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncInj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (leftInvIsSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjCantorThm) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (foundation2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSclos) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peano0notS) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peanoSinj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ordinalMinLem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (!!) @ (
% 122.49/16.36                                                                     ^[Y0 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (ordinal @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y1 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y2 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y2 @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ 
% 122.49/16.36                                                                      Y2) =>
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.36      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl864])).
% 122.49/16.36  thf(zip_derived_cl879, plain,
% 122.49/16.36      (~ (((powersetE1) =>
% 122.49/16.36           (((inPowerset) =>
% 122.49/16.36             (((powersetsubset) =>
% 122.49/16.36               (((sepInPowerset) =>
% 122.49/16.36                 (((sepSubset) =>
% 122.49/16.36                   (((binunionIL) =>
% 122.49/16.36                     (((upairset2IR) =>
% 122.49/16.36                       (((binunionIR) =>
% 122.49/16.36                         (((binunionEcases) =>
% 122.49/16.36                           (((binunionE) =>
% 122.49/16.36                             (((binunionLsub) =>
% 122.49/16.36                               (((binunionRsub) =>
% 122.49/16.36                                 (((binintersectI) =>
% 122.49/16.36                                   (((binintersectSubset5) =>
% 122.49/16.36                                     (((binintersectEL) =>
% 122.49/16.36                                       (((binintersectLsub) =>
% 122.49/16.36                                         (((binintersectSubset2) =>
% 122.49/16.36                                           (((binintersectSubset3) =>
% 122.49/16.36                                             (((binintersectER) =>
% 122.49/16.36                                               (((disjointsetsI1) =>
% 122.49/16.36                                                 (((binintersectRsub) =>
% 122.49/16.36                                                   (((binintersectSubset4) =>
% 122.49/16.36                                                     (((binintersectSubset1) =>
% 122.49/16.36                                                       (((bs114d) =>
% 122.49/16.36                                                         (((setminusI) =>
% 122.49/16.36                                                           (((setminusEL) =>
% 122.49/16.36                                                             (((setminusER) =>
% 122.49/16.36                                                               (((setminusSubset2) =>
% 122.49/16.36                                                                 (((setminusERneg) =>
% 122.49/16.36                                                                   (((setminusELneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusILneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusIRneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusLsub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusSubset1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (secondinupair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairiskpair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowerset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairset2E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairsubunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairinpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionE2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsuniq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR11) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR12) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairequniteq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemEL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempaircEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrSub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrERa) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcImageSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (apProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (app) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (infuncsetfunc) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcinfuncset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcextLem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2lamEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theeq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrue) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueorfalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setextT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subsetTI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTELcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTERcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTnotintersectT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementImpComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contraSubsetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTcontraSubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTILcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTIRcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTEcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule0) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_5) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1SetBreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (choice2fnsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compEex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionEcases) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionCommutes) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2W) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2A) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2B) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Equiv) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncInj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (leftInvIsSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjCantorThm) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (foundation2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSclos) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peano0notS) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peanoSinj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ordinalMinLem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (!!) @ (
% 122.49/16.36                                                                     ^[Y0 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (ordinal @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y1 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y2 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y2 @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ 
% 122.49/16.36                                                                      Y2) =>
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.36      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl872])).
% 122.49/16.36  thf(zip_derived_cl886, plain,
% 122.49/16.36      (~ (((inPowerset) =>
% 122.49/16.36           (((powersetsubset) =>
% 122.49/16.36             (((sepInPowerset) =>
% 122.49/16.36               (((sepSubset) =>
% 122.49/16.36                 (((binunionIL) =>
% 122.49/16.36                   (((upairset2IR) =>
% 122.49/16.36                     (((binunionIR) =>
% 122.49/16.36                       (((binunionEcases) =>
% 122.49/16.36                         (((binunionE) =>
% 122.49/16.36                           (((binunionLsub) =>
% 122.49/16.36                             (((binunionRsub) =>
% 122.49/16.36                               (((binintersectI) =>
% 122.49/16.36                                 (((binintersectSubset5) =>
% 122.49/16.36                                   (((binintersectEL) =>
% 122.49/16.36                                     (((binintersectLsub) =>
% 122.49/16.36                                       (((binintersectSubset2) =>
% 122.49/16.36                                         (((binintersectSubset3) =>
% 122.49/16.36                                           (((binintersectER) =>
% 122.49/16.36                                             (((disjointsetsI1) =>
% 122.49/16.36                                               (((binintersectRsub) =>
% 122.49/16.36                                                 (((binintersectSubset4) =>
% 122.49/16.36                                                   (((binintersectSubset1) =>
% 122.49/16.36                                                     (((bs114d) =>
% 122.49/16.36                                                       (((setminusI) =>
% 122.49/16.36                                                         (((setminusEL) =>
% 122.49/16.36                                                           (((setminusER) =>
% 122.49/16.36                                                             (((setminusSubset2) =>
% 122.49/16.36                                                               (((setminusERneg) =>
% 122.49/16.36                                                                 (((setminusELneg) =>
% 122.49/16.36                                                                   (((setminusILneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusIRneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusLsub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusSubset1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (secondinupair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairiskpair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowerset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairset2E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairsubunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairinpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionE2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsuniq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR11) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR12) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairequniteq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemEL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempaircEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrSub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrERa) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcImageSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (apProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (app) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (infuncsetfunc) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcinfuncset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcextLem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2lamEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theeq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrue) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueorfalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setextT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subsetTI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTELcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTERcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTnotintersectT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementImpComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contraSubsetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTcontraSubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTILcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTIRcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTEcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule0) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_5) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1SetBreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (choice2fnsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compEex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionEcases) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionCommutes) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2W) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2A) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2B) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Equiv) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncInj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (leftInvIsSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjCantorThm) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (foundation2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSclos) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peano0notS) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peanoSinj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ordinalMinLem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (!!) @ (
% 122.49/16.36                                                                     ^[Y0 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (ordinal @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y1 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y2 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y2 @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ 
% 122.49/16.36                                                                      Y2) =>
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.36      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl879])).
% 122.49/16.36  thf(zip_derived_cl892, plain,
% 122.49/16.36      (~ (((powersetsubset) =>
% 122.49/16.36           (((sepInPowerset) =>
% 122.49/16.36             (((sepSubset) =>
% 122.49/16.36               (((binunionIL) =>
% 122.49/16.36                 (((upairset2IR) =>
% 122.49/16.36                   (((binunionIR) =>
% 122.49/16.36                     (((binunionEcases) =>
% 122.49/16.36                       (((binunionE) =>
% 122.49/16.36                         (((binunionLsub) =>
% 122.49/16.36                           (((binunionRsub) =>
% 122.49/16.36                             (((binintersectI) =>
% 122.49/16.36                               (((binintersectSubset5) =>
% 122.49/16.36                                 (((binintersectEL) =>
% 122.49/16.36                                   (((binintersectLsub) =>
% 122.49/16.36                                     (((binintersectSubset2) =>
% 122.49/16.36                                       (((binintersectSubset3) =>
% 122.49/16.36                                         (((binintersectER) =>
% 122.49/16.36                                           (((disjointsetsI1) =>
% 122.49/16.36                                             (((binintersectRsub) =>
% 122.49/16.36                                               (((binintersectSubset4) =>
% 122.49/16.36                                                 (((binintersectSubset1) =>
% 122.49/16.36                                                   (((bs114d) =>
% 122.49/16.36                                                     (((setminusI) =>
% 122.49/16.36                                                       (((setminusEL) =>
% 122.49/16.36                                                         (((setminusER) =>
% 122.49/16.36                                                           (((setminusSubset2) =>
% 122.49/16.36                                                             (((setminusERneg) =>
% 122.49/16.36                                                               (((setminusELneg) =>
% 122.49/16.36                                                                 (((setminusILneg) =>
% 122.49/16.36                                                                   (((setminusIRneg) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusLsub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusSubset1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (secondinupair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairiskpair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowerset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairset2E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairsubunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairinpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionE2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsuniq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR11) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR12) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairequniteq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemEL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempaircEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrSub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrERa) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcImageSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (apProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (app) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (infuncsetfunc) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcinfuncset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcextLem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2lamEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theeq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrue) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueorfalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setextT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subsetTI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTELcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTERcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTnotintersectT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementImpComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contraSubsetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTcontraSubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTILcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTIRcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTEcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule0) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_5) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1SetBreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (choice2fnsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compEex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionEcases) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionCommutes) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2W) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2A) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2B) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Equiv) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncInj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (leftInvIsSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjCantorThm) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (foundation2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSclos) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peano0notS) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peanoSinj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ordinalMinLem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (!!) @ (
% 122.49/16.36                                                                     ^[Y0 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (ordinal @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y1 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y2 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y2 @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ 
% 122.49/16.36                                                                      Y2) =>
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.36      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl886])).
% 122.49/16.36  thf(zip_derived_cl899, plain,
% 122.49/16.36      (~ (((sepInPowerset) =>
% 122.49/16.36           (((sepSubset) =>
% 122.49/16.36             (((binunionIL) =>
% 122.49/16.36               (((upairset2IR) =>
% 122.49/16.36                 (((binunionIR) =>
% 122.49/16.36                   (((binunionEcases) =>
% 122.49/16.36                     (((binunionE) =>
% 122.49/16.36                       (((binunionLsub) =>
% 122.49/16.36                         (((binunionRsub) =>
% 122.49/16.36                           (((binintersectI) =>
% 122.49/16.36                             (((binintersectSubset5) =>
% 122.49/16.36                               (((binintersectEL) =>
% 122.49/16.36                                 (((binintersectLsub) =>
% 122.49/16.36                                   (((binintersectSubset2) =>
% 122.49/16.36                                     (((binintersectSubset3) =>
% 122.49/16.36                                       (((binintersectER) =>
% 122.49/16.36                                         (((disjointsetsI1) =>
% 122.49/16.36                                           (((binintersectRsub) =>
% 122.49/16.36                                             (((binintersectSubset4) =>
% 122.49/16.36                                               (((binintersectSubset1) =>
% 122.49/16.36                                                 (((bs114d) =>
% 122.49/16.36                                                   (((setminusI) =>
% 122.49/16.36                                                     (((setminusEL) =>
% 122.49/16.36                                                       (((setminusER) =>
% 122.49/16.36                                                         (((setminusSubset2) =>
% 122.49/16.36                                                           (((setminusERneg) =>
% 122.49/16.36                                                             (((setminusELneg) =>
% 122.49/16.36                                                               (((setminusILneg) =>
% 122.49/16.36                                                                 (((setminusIRneg) =>
% 122.49/16.36                                                                   (((setminusLsub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusSubset1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (secondinupair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairiskpair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowerset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairset2E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairsubunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairinpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionE2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsuniq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR11) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR12) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairequniteq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemEL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempaircEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrSub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrERa) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcImageSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (apProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (app) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (infuncsetfunc) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcinfuncset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcextLem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2lamEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theeq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrue) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueorfalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setextT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subsetTI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTELcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTERcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTnotintersectT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementImpComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contraSubsetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTcontraSubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTILcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTIRcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTEcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule0) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_5) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1SetBreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (choice2fnsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compEex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionEcases) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionCommutes) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2W) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2A) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2B) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Equiv) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncInj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (leftInvIsSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjCantorThm) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (foundation2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSclos) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peano0notS) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peanoSinj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ordinalMinLem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (!!) @ (
% 122.49/16.36                                                                     ^[Y0 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (ordinal @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y1 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y2 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y2 @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ 
% 122.49/16.36                                                                      Y2) =>
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.36      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl892])).
% 122.49/16.36  thf(zip_derived_cl906, plain,
% 122.49/16.36      (~ (((sepSubset) =>
% 122.49/16.36           (((binunionIL) =>
% 122.49/16.36             (((upairset2IR) =>
% 122.49/16.36               (((binunionIR) =>
% 122.49/16.36                 (((binunionEcases) =>
% 122.49/16.36                   (((binunionE) =>
% 122.49/16.36                     (((binunionLsub) =>
% 122.49/16.36                       (((binunionRsub) =>
% 122.49/16.36                         (((binintersectI) =>
% 122.49/16.36                           (((binintersectSubset5) =>
% 122.49/16.36                             (((binintersectEL) =>
% 122.49/16.36                               (((binintersectLsub) =>
% 122.49/16.36                                 (((binintersectSubset2) =>
% 122.49/16.36                                   (((binintersectSubset3) =>
% 122.49/16.36                                     (((binintersectER) =>
% 122.49/16.36                                       (((disjointsetsI1) =>
% 122.49/16.36                                         (((binintersectRsub) =>
% 122.49/16.36                                           (((binintersectSubset4) =>
% 122.49/16.36                                             (((binintersectSubset1) =>
% 122.49/16.36                                               (((bs114d) =>
% 122.49/16.36                                                 (((setminusI) =>
% 122.49/16.36                                                   (((setminusEL) =>
% 122.49/16.36                                                     (((setminusER) =>
% 122.49/16.36                                                       (((setminusSubset2) =>
% 122.49/16.36                                                         (((setminusERneg) =>
% 122.49/16.36                                                           (((setminusELneg) =>
% 122.49/16.36                                                             (((setminusILneg) =>
% 122.49/16.36                                                               (((setminusIRneg) =>
% 122.49/16.36                                                                 (((setminusLsub) =>
% 122.49/16.36                                                                   (((setminusSubset1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (secondinupair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairiskpair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowerset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairset2E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairsubunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairinpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionE2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsuniq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR11) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR12) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairequniteq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemEL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempaircEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrSub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrERa) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcImageSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (apProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (app) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (infuncsetfunc) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcinfuncset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcextLem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2lamEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theeq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrue) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueorfalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setextT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subsetTI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTELcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTERcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTnotintersectT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementImpComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contraSubsetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTcontraSubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTILcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTIRcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTEcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule0) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_5) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1SetBreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (choice2fnsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compEex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionEcases) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionCommutes) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2W) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2A) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2B) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Equiv) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncInj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (leftInvIsSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjCantorThm) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (foundation2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSclos) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peano0notS) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peanoSinj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ordinalMinLem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (!!) @ (
% 122.49/16.36                                                                     ^[Y0 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (ordinal @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y1 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y2 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y2 @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ 
% 122.49/16.36                                                                      Y2) =>
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.36      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl899])).
% 122.49/16.36  thf(zip_derived_cl911, plain,
% 122.49/16.36      (~ (((binunionIL) =>
% 122.49/16.36           (((upairset2IR) =>
% 122.49/16.36             (((binunionIR) =>
% 122.49/16.36               (((binunionEcases) =>
% 122.49/16.36                 (((binunionE) =>
% 122.49/16.36                   (((binunionLsub) =>
% 122.49/16.36                     (((binunionRsub) =>
% 122.49/16.36                       (((binintersectI) =>
% 122.49/16.36                         (((binintersectSubset5) =>
% 122.49/16.36                           (((binintersectEL) =>
% 122.49/16.36                             (((binintersectLsub) =>
% 122.49/16.36                               (((binintersectSubset2) =>
% 122.49/16.36                                 (((binintersectSubset3) =>
% 122.49/16.36                                   (((binintersectER) =>
% 122.49/16.36                                     (((disjointsetsI1) =>
% 122.49/16.36                                       (((binintersectRsub) =>
% 122.49/16.36                                         (((binintersectSubset4) =>
% 122.49/16.36                                           (((binintersectSubset1) =>
% 122.49/16.36                                             (((bs114d) =>
% 122.49/16.36                                               (((setminusI) =>
% 122.49/16.36                                                 (((setminusEL) =>
% 122.49/16.36                                                   (((setminusER) =>
% 122.49/16.36                                                     (((setminusSubset2) =>
% 122.49/16.36                                                       (((setminusERneg) =>
% 122.49/16.36                                                         (((setminusELneg) =>
% 122.49/16.36                                                           (((setminusILneg) =>
% 122.49/16.36                                                             (((setminusIRneg) =>
% 122.49/16.36                                                               (((setminusLsub) =>
% 122.49/16.36                                                                 (((setminusSubset1) =>
% 122.49/16.36                                                                   (((symdiffE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (secondinupair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairiskpair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowerset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairset2E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairsubunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairinpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionE2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsuniq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR11) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR12) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairequniteq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemEL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempaircEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrSub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrERa) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcImageSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (apProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (app) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (infuncsetfunc) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcinfuncset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcextLem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2lamEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theeq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrue) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueorfalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setextT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subsetTI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTELcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTERcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTnotintersectT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementImpComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contraSubsetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTcontraSubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTILcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTIRcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTEcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule0) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_5) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1SetBreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (choice2fnsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compEex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionEcases) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionCommutes) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2W) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2A) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2B) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Equiv) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncInj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (leftInvIsSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjCantorThm) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (foundation2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSclos) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peano0notS) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peanoSinj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ordinalMinLem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (!!) @ (
% 122.49/16.36                                                                     ^[Y0 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (ordinal @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y1 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y2 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y2 @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ 
% 122.49/16.36                                                                      Y2) =>
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.36      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl906])).
% 122.49/16.36  thf(zip_derived_cl917, plain,
% 122.49/16.36      (~ (((upairset2IR) =>
% 122.49/16.36           (((binunionIR) =>
% 122.49/16.36             (((binunionEcases) =>
% 122.49/16.36               (((binunionE) =>
% 122.49/16.36                 (((binunionLsub) =>
% 122.49/16.36                   (((binunionRsub) =>
% 122.49/16.36                     (((binintersectI) =>
% 122.49/16.36                       (((binintersectSubset5) =>
% 122.49/16.36                         (((binintersectEL) =>
% 122.49/16.36                           (((binintersectLsub) =>
% 122.49/16.36                             (((binintersectSubset2) =>
% 122.49/16.36                               (((binintersectSubset3) =>
% 122.49/16.36                                 (((binintersectER) =>
% 122.49/16.36                                   (((disjointsetsI1) =>
% 122.49/16.36                                     (((binintersectRsub) =>
% 122.49/16.36                                       (((binintersectSubset4) =>
% 122.49/16.36                                         (((binintersectSubset1) =>
% 122.49/16.36                                           (((bs114d) =>
% 122.49/16.36                                             (((setminusI) =>
% 122.49/16.36                                               (((setminusEL) =>
% 122.49/16.36                                                 (((setminusER) =>
% 122.49/16.36                                                   (((setminusSubset2) =>
% 122.49/16.36                                                     (((setminusERneg) =>
% 122.49/16.36                                                       (((setminusELneg) =>
% 122.49/16.36                                                         (((setminusILneg) =>
% 122.49/16.36                                                           (((setminusIRneg) =>
% 122.49/16.36                                                             (((setminusLsub) =>
% 122.49/16.36                                                               (((setminusSubset1) =>
% 122.49/16.36                                                                 (((symdiffE) =>
% 122.49/16.36                                                                   (((symdiffI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffI2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (secondinupair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairiskpair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowerset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairset2E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairsubunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairinpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionE2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsuniq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR11) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR12) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairequniteq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemEL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempaircEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrSub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrERa) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcImageSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (apProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (app) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (infuncsetfunc) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcinfuncset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcextLem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2lamEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theeq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrue) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueorfalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setextT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subsetTI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTELcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTERcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTnotintersectT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementImpComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contraSubsetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTcontraSubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTILcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTIRcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTEcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule0) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_5) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1SetBreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (choice2fnsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compEex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionEcases) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionCommutes) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2W) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2A) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2B) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Equiv) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncInj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (leftInvIsSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjCantorThm) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (foundation2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSclos) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peano0notS) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peanoSinj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ordinalMinLem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (!!) @ (
% 122.49/16.36                                                                     ^[Y0 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (ordinal @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y1 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y2 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y2 @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ 
% 122.49/16.36                                                                      Y2) =>
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.36      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl911])).
% 122.49/16.36  thf(zip_derived_cl924, plain,
% 122.49/16.36      (~ (((binunionIR) =>
% 122.49/16.36           (((binunionEcases) =>
% 122.49/16.36             (((binunionE) =>
% 122.49/16.36               (((binunionLsub) =>
% 122.49/16.36                 (((binunionRsub) =>
% 122.49/16.36                   (((binintersectI) =>
% 122.49/16.36                     (((binintersectSubset5) =>
% 122.49/16.36                       (((binintersectEL) =>
% 122.49/16.36                         (((binintersectLsub) =>
% 122.49/16.36                           (((binintersectSubset2) =>
% 122.49/16.36                             (((binintersectSubset3) =>
% 122.49/16.36                               (((binintersectER) =>
% 122.49/16.36                                 (((disjointsetsI1) =>
% 122.49/16.36                                   (((binintersectRsub) =>
% 122.49/16.36                                     (((binintersectSubset4) =>
% 122.49/16.36                                       (((binintersectSubset1) =>
% 122.49/16.36                                         (((bs114d) =>
% 122.49/16.36                                           (((setminusI) =>
% 122.49/16.36                                             (((setminusEL) =>
% 122.49/16.36                                               (((setminusER) =>
% 122.49/16.36                                                 (((setminusSubset2) =>
% 122.49/16.36                                                   (((setminusERneg) =>
% 122.49/16.36                                                     (((setminusELneg) =>
% 122.49/16.36                                                       (((setminusILneg) =>
% 122.49/16.36                                                         (((setminusIRneg) =>
% 122.49/16.36                                                           (((setminusLsub) =>
% 122.49/16.36                                                             (((setminusSubset1) =>
% 122.49/16.36                                                               (((symdiffE) =>
% 122.49/16.36                                                                 (((symdiffI1) =>
% 122.49/16.36                                                                   (((symdiffI2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (secondinupair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairiskpair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowerset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairset2E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairsubunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairinpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionE2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsuniq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR11) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR12) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairequniteq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemEL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempaircEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrSub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrERa) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcImageSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (apProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (app) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (infuncsetfunc) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcinfuncset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcextLem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2lamEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theeq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrue) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueorfalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setextT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subsetTI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTELcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTERcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTnotintersectT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementImpComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contraSubsetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTcontraSubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTILcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTIRcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTEcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule0) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_5) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1SetBreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (choice2fnsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compEex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionEcases) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionCommutes) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2W) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2A) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2B) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Equiv) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncInj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (leftInvIsSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjCantorThm) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (foundation2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSclos) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peano0notS) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peanoSinj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ordinalMinLem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (!!) @ (
% 122.49/16.36                                                                     ^[Y0 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (ordinal @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y1 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y2 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y2 @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ 
% 122.49/16.36                                                                      Y2) =>
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.36      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl917])).
% 122.49/16.36  thf(zip_derived_cl929, plain,
% 122.49/16.36      (~ (((binunionEcases) =>
% 122.49/16.36           (((binunionE) =>
% 122.49/16.36             (((binunionLsub) =>
% 122.49/16.36               (((binunionRsub) =>
% 122.49/16.36                 (((binintersectI) =>
% 122.49/16.36                   (((binintersectSubset5) =>
% 122.49/16.36                     (((binintersectEL) =>
% 122.49/16.36                       (((binintersectLsub) =>
% 122.49/16.36                         (((binintersectSubset2) =>
% 122.49/16.36                           (((binintersectSubset3) =>
% 122.49/16.36                             (((binintersectER) =>
% 122.49/16.36                               (((disjointsetsI1) =>
% 122.49/16.36                                 (((binintersectRsub) =>
% 122.49/16.36                                   (((binintersectSubset4) =>
% 122.49/16.36                                     (((binintersectSubset1) =>
% 122.49/16.36                                       (((bs114d) =>
% 122.49/16.36                                         (((setminusI) =>
% 122.49/16.36                                           (((setminusEL) =>
% 122.49/16.36                                             (((setminusER) =>
% 122.49/16.36                                               (((setminusSubset2) =>
% 122.49/16.36                                                 (((setminusERneg) =>
% 122.49/16.36                                                   (((setminusELneg) =>
% 122.49/16.36                                                     (((setminusILneg) =>
% 122.49/16.36                                                       (((setminusIRneg) =>
% 122.49/16.36                                                         (((setminusLsub) =>
% 122.49/16.36                                                           (((setminusSubset1) =>
% 122.49/16.36                                                             (((symdiffE) =>
% 122.49/16.36                                                               (((symdiffI1) =>
% 122.49/16.36                                                                 (((symdiffI2) =>
% 122.49/16.36                                                                   (((symdiffIneg1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (symdiffIneg2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (secondinupair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairiskpair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowerset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairset2E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairsubunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairinpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionE2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsuniq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR11) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR12) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairequniteq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ksndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemEL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairmemER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempaircEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodsndpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairsurjEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrSub) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrERa) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrEL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (dpsetconstrER) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcImageSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (apProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (app) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (infuncsetfunc) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcinfuncset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamProp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lamp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2p) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (brelnall2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcextLem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcGraphProp4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (funcext2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ap2apEq2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (lam2lamEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (beta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eta2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalseProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueProp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifSingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ifp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theeq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrue) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iffalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (iftrueorfalse) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setminusT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementT_lem) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setextT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subsetTI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (powersetTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTELcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintersectTERcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contrasubsetT3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementI1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementE1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementSub2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (doubleComplementEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTnotintersectT) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementImpComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (contraSubsetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementTcontraSubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTILcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTIRcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binunionTEcontra) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2a) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2b) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (demorgan2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule0) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz13rule4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_4) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz1_5) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1SetBreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (choice2fnsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1all1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (subbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (eqbreln1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1invE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1compEex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionI) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionE) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionEcases) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (breln1unionCommutes) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2W) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2A) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (woz2B) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Ex1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1Equiv) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (image1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (injFuncSetFuncInj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (leftInvIsSurj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (surjCantorThm) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (foundation2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (notinself2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (omegaSclos) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peano0notS) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (peanoSinj) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (binintTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (transitivesetOp2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionTransitive) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ordinalMinLem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (!!) @ (
% 122.49/16.36                                                                     ^[Y0 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (ordinal @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y1 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (!!) @ (
% 122.49/16.36                                                                      ^[Y2 : $i]:
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y2 @ 
% 122.49/16.36                                                                      Y0) =>
% 122.49/16.36                                                                      ((
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ 
% 122.49/16.36                                                                      Y2) =>
% 122.49/16.36                                                                      (in @ 
% 122.49/16.36                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.36      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl924])).
% 122.49/16.36  thf(zip_derived_cl934, plain,
% 122.49/16.36      (~ (((binunionE) =>
% 122.49/16.36           (((binunionLsub) =>
% 122.49/16.36             (((binunionRsub) =>
% 122.49/16.36               (((binintersectI) =>
% 122.49/16.36                 (((binintersectSubset5) =>
% 122.49/16.36                   (((binintersectEL) =>
% 122.49/16.36                     (((binintersectLsub) =>
% 122.49/16.36                       (((binintersectSubset2) =>
% 122.49/16.36                         (((binintersectSubset3) =>
% 122.49/16.36                           (((binintersectER) =>
% 122.49/16.36                             (((disjointsetsI1) =>
% 122.49/16.36                               (((binintersectRsub) =>
% 122.49/16.36                                 (((binintersectSubset4) =>
% 122.49/16.36                                   (((binintersectSubset1) =>
% 122.49/16.36                                     (((bs114d) =>
% 122.49/16.36                                       (((setminusI) =>
% 122.49/16.36                                         (((setminusEL) =>
% 122.49/16.36                                           (((setminusER) =>
% 122.49/16.36                                             (((setminusSubset2) =>
% 122.49/16.36                                               (((setminusERneg) =>
% 122.49/16.36                                                 (((setminusELneg) =>
% 122.49/16.36                                                   (((setminusILneg) =>
% 122.49/16.36                                                     (((setminusIRneg) =>
% 122.49/16.36                                                       (((setminusLsub) =>
% 122.49/16.36                                                         (((setminusSubset1) =>
% 122.49/16.36                                                           (((symdiffE) =>
% 122.49/16.36                                                             (((symdiffI1) =>
% 122.49/16.36                                                               (((symdiffI2) =>
% 122.49/16.36                                                                 (((symdiffIneg1) =>
% 122.49/16.36                                                                   (((symdiffIneg2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (secondinupair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairIR) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairiskpair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kpairp) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsubset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowerset) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletoninpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairset2E) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairsubunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairinpowunion) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ubforcartprodlem3) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodpairin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodmempair) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionE2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setunionsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1E1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (ex1I2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (singletonsuniq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstsingleton) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (theprop) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (kfstpairEq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (cartprodfstin) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL2) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjL) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR11) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR12) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR1) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (upairequniteq) =>
% 122.49/16.36                                                                     ((
% 122.49/16.36                                                                     (setukpairinjR2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemEL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempaircEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrSub) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrERa) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcImageSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (apProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (app) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (infuncsetfunc) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcinfuncset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcextLem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2lamEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theeq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrue) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueorfalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setminusT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setextT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subsetTI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTELcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTERcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTnotintersectT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementImpComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contraSubsetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTcontraSubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTILcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTIRcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTEcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule0) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_5) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1SetBreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (choice2fnsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compEex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionEcases) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionCommutes) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2W) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2A) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2B) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Equiv) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncInj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (leftInvIsSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjCantorThm) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (foundation2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSclos) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peano0notS) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peanoSinj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ordinalMinLem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (!!) @ (
% 122.49/16.37                                                                     ^[Y0 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (ordinal @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y1 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y2 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y2 @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ 
% 122.49/16.37                                                                      Y2) =>
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.37      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl929])).
% 122.49/16.37  thf(zip_derived_cl940, plain,
% 122.49/16.37      (~ (((binunionLsub) =>
% 122.49/16.37           (((binunionRsub) =>
% 122.49/16.37             (((binintersectI) =>
% 122.49/16.37               (((binintersectSubset5) =>
% 122.49/16.37                 (((binintersectEL) =>
% 122.49/16.37                   (((binintersectLsub) =>
% 122.49/16.37                     (((binintersectSubset2) =>
% 122.49/16.37                       (((binintersectSubset3) =>
% 122.49/16.37                         (((binintersectER) =>
% 122.49/16.37                           (((disjointsetsI1) =>
% 122.49/16.37                             (((binintersectRsub) =>
% 122.49/16.37                               (((binintersectSubset4) =>
% 122.49/16.37                                 (((binintersectSubset1) =>
% 122.49/16.37                                   (((bs114d) =>
% 122.49/16.37                                     (((setminusI) =>
% 122.49/16.37                                       (((setminusEL) =>
% 122.49/16.37                                         (((setminusER) =>
% 122.49/16.37                                           (((setminusSubset2) =>
% 122.49/16.37                                             (((setminusERneg) =>
% 122.49/16.37                                               (((setminusELneg) =>
% 122.49/16.37                                                 (((setminusILneg) =>
% 122.49/16.37                                                   (((setminusIRneg) =>
% 122.49/16.37                                                     (((setminusLsub) =>
% 122.49/16.37                                                       (((setminusSubset1) =>
% 122.49/16.37                                                         (((symdiffE) =>
% 122.49/16.37                                                           (((symdiffI1) =>
% 122.49/16.37                                                             (((symdiffI2) =>
% 122.49/16.37                                                               (((symdiffIneg1) =>
% 122.49/16.37                                                                 (((symdiffIneg2) =>
% 122.49/16.37                                                                   (((secondinupair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairiskpair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowerset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairset2E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairsubunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairinpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionE2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsuniq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR11) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR12) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairequniteq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemEL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempaircEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrSub) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrERa) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcImageSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (apProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (app) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (infuncsetfunc) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcinfuncset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcextLem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2lamEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theeq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrue) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueorfalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setminusT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setextT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subsetTI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTELcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTERcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTnotintersectT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementImpComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contraSubsetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTcontraSubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTILcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTIRcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTEcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule0) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_5) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1SetBreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (choice2fnsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compEex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionEcases) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionCommutes) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2W) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2A) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2B) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Equiv) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncInj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (leftInvIsSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjCantorThm) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (foundation2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSclos) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peano0notS) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peanoSinj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ordinalMinLem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (!!) @ (
% 122.49/16.37                                                                     ^[Y0 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (ordinal @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y1 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y2 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y2 @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ 
% 122.49/16.37                                                                      Y2) =>
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.37      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl934])).
% 122.49/16.37  thf(zip_derived_cl945, plain,
% 122.49/16.37      (~ (((binunionRsub) =>
% 122.49/16.37           (((binintersectI) =>
% 122.49/16.37             (((binintersectSubset5) =>
% 122.49/16.37               (((binintersectEL) =>
% 122.49/16.37                 (((binintersectLsub) =>
% 122.49/16.37                   (((binintersectSubset2) =>
% 122.49/16.37                     (((binintersectSubset3) =>
% 122.49/16.37                       (((binintersectER) =>
% 122.49/16.37                         (((disjointsetsI1) =>
% 122.49/16.37                           (((binintersectRsub) =>
% 122.49/16.37                             (((binintersectSubset4) =>
% 122.49/16.37                               (((binintersectSubset1) =>
% 122.49/16.37                                 (((bs114d) =>
% 122.49/16.37                                   (((setminusI) =>
% 122.49/16.37                                     (((setminusEL) =>
% 122.49/16.37                                       (((setminusER) =>
% 122.49/16.37                                         (((setminusSubset2) =>
% 122.49/16.37                                           (((setminusERneg) =>
% 122.49/16.37                                             (((setminusELneg) =>
% 122.49/16.37                                               (((setminusILneg) =>
% 122.49/16.37                                                 (((setminusIRneg) =>
% 122.49/16.37                                                   (((setminusLsub) =>
% 122.49/16.37                                                     (((setminusSubset1) =>
% 122.49/16.37                                                       (((symdiffE) =>
% 122.49/16.37                                                         (((symdiffI1) =>
% 122.49/16.37                                                           (((symdiffI2) =>
% 122.49/16.37                                                             (((symdiffIneg1) =>
% 122.49/16.37                                                               (((symdiffIneg2) =>
% 122.49/16.37                                                                 (((secondinupair) =>
% 122.49/16.37                                                                   (((setukpairIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairiskpair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowerset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairset2E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairsubunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairinpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionE2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsuniq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR11) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR12) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairequniteq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemEL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempaircEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrSub) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrERa) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcImageSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (apProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (app) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (infuncsetfunc) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcinfuncset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcextLem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2lamEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theeq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrue) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueorfalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setminusT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setextT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subsetTI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTELcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTERcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTnotintersectT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementImpComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contraSubsetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTcontraSubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTILcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTIRcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTEcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule0) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_5) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1SetBreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (choice2fnsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compEex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionEcases) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionCommutes) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2W) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2A) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2B) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Equiv) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncInj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (leftInvIsSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjCantorThm) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (foundation2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSclos) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peano0notS) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peanoSinj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ordinalMinLem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (!!) @ (
% 122.49/16.37                                                                     ^[Y0 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (ordinal @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y1 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y2 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y2 @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ 
% 122.49/16.37                                                                      Y2) =>
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.37      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl940])).
% 122.49/16.37  thf(zip_derived_cl951, plain,
% 122.49/16.37      (~ (((binintersectI) =>
% 122.49/16.37           (((binintersectSubset5) =>
% 122.49/16.37             (((binintersectEL) =>
% 122.49/16.37               (((binintersectLsub) =>
% 122.49/16.37                 (((binintersectSubset2) =>
% 122.49/16.37                   (((binintersectSubset3) =>
% 122.49/16.37                     (((binintersectER) =>
% 122.49/16.37                       (((disjointsetsI1) =>
% 122.49/16.37                         (((binintersectRsub) =>
% 122.49/16.37                           (((binintersectSubset4) =>
% 122.49/16.37                             (((binintersectSubset1) =>
% 122.49/16.37                               (((bs114d) =>
% 122.49/16.37                                 (((setminusI) =>
% 122.49/16.37                                   (((setminusEL) =>
% 122.49/16.37                                     (((setminusER) =>
% 122.49/16.37                                       (((setminusSubset2) =>
% 122.49/16.37                                         (((setminusERneg) =>
% 122.49/16.37                                           (((setminusELneg) =>
% 122.49/16.37                                             (((setminusILneg) =>
% 122.49/16.37                                               (((setminusIRneg) =>
% 122.49/16.37                                                 (((setminusLsub) =>
% 122.49/16.37                                                   (((setminusSubset1) =>
% 122.49/16.37                                                     (((symdiffE) =>
% 122.49/16.37                                                       (((symdiffI1) =>
% 122.49/16.37                                                         (((symdiffI2) =>
% 122.49/16.37                                                           (((symdiffIneg1) =>
% 122.49/16.37                                                             (((symdiffIneg2) =>
% 122.49/16.37                                                               (((secondinupair) =>
% 122.49/16.37                                                                 (((setukpairIL) =>
% 122.49/16.37                                                                   (((setukpairIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairiskpair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowerset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairset2E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairsubunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairinpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionE2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsuniq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR11) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR12) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairequniteq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemEL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempaircEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrSub) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrERa) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcImageSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (apProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (app) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (infuncsetfunc) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcinfuncset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcextLem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2lamEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theeq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrue) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueorfalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setminusT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setextT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subsetTI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTELcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTERcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTnotintersectT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementImpComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contraSubsetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTcontraSubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTILcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTIRcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTEcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule0) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_5) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1SetBreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (choice2fnsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compEex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionEcases) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionCommutes) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2W) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2A) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2B) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Equiv) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncInj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (leftInvIsSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjCantorThm) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (foundation2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSclos) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peano0notS) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peanoSinj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ordinalMinLem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (!!) @ (
% 122.49/16.37                                                                     ^[Y0 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (ordinal @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y1 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y2 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y2 @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ 
% 122.49/16.37                                                                      Y2) =>
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.37      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl945])).
% 122.49/16.37  thf(zip_derived_cl957, plain,
% 122.49/16.37      (~ (((binintersectSubset5) =>
% 122.49/16.37           (((binintersectEL) =>
% 122.49/16.37             (((binintersectLsub) =>
% 122.49/16.37               (((binintersectSubset2) =>
% 122.49/16.37                 (((binintersectSubset3) =>
% 122.49/16.37                   (((binintersectER) =>
% 122.49/16.37                     (((disjointsetsI1) =>
% 122.49/16.37                       (((binintersectRsub) =>
% 122.49/16.37                         (((binintersectSubset4) =>
% 122.49/16.37                           (((binintersectSubset1) =>
% 122.49/16.37                             (((bs114d) =>
% 122.49/16.37                               (((setminusI) =>
% 122.49/16.37                                 (((setminusEL) =>
% 122.49/16.37                                   (((setminusER) =>
% 122.49/16.37                                     (((setminusSubset2) =>
% 122.49/16.37                                       (((setminusERneg) =>
% 122.49/16.37                                         (((setminusELneg) =>
% 122.49/16.37                                           (((setminusILneg) =>
% 122.49/16.37                                             (((setminusIRneg) =>
% 122.49/16.37                                               (((setminusLsub) =>
% 122.49/16.37                                                 (((setminusSubset1) =>
% 122.49/16.37                                                   (((symdiffE) =>
% 122.49/16.37                                                     (((symdiffI1) =>
% 122.49/16.37                                                       (((symdiffI2) =>
% 122.49/16.37                                                         (((symdiffIneg1) =>
% 122.49/16.37                                                           (((symdiffIneg2) =>
% 122.49/16.37                                                             (((secondinupair) =>
% 122.49/16.37                                                               (((setukpairIL) =>
% 122.49/16.37                                                                 (((setukpairIR) =>
% 122.49/16.37                                                                   (((kpairiskpair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowerset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairset2E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairsubunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairinpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionE2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsuniq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR11) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR12) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairequniteq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemEL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempaircEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrSub) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrERa) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcImageSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (apProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (app) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (infuncsetfunc) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcinfuncset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcextLem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2lamEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theeq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrue) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueorfalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setminusT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setextT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subsetTI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTELcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTERcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTnotintersectT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementImpComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contraSubsetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTcontraSubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTILcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTIRcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTEcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule0) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_5) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1SetBreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (choice2fnsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compEex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionEcases) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionCommutes) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2W) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2A) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2B) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Equiv) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncInj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (leftInvIsSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjCantorThm) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (foundation2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSclos) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peano0notS) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peanoSinj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ordinalMinLem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (!!) @ (
% 122.49/16.37                                                                     ^[Y0 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (ordinal @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y1 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y2 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y2 @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ 
% 122.49/16.37                                                                      Y2) =>
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.37      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl951])).
% 122.49/16.37  thf(zip_derived_cl964, plain,
% 122.49/16.37      (~ (((binintersectEL) =>
% 122.49/16.37           (((binintersectLsub) =>
% 122.49/16.37             (((binintersectSubset2) =>
% 122.49/16.37               (((binintersectSubset3) =>
% 122.49/16.37                 (((binintersectER) =>
% 122.49/16.37                   (((disjointsetsI1) =>
% 122.49/16.37                     (((binintersectRsub) =>
% 122.49/16.37                       (((binintersectSubset4) =>
% 122.49/16.37                         (((binintersectSubset1) =>
% 122.49/16.37                           (((bs114d) =>
% 122.49/16.37                             (((setminusI) =>
% 122.49/16.37                               (((setminusEL) =>
% 122.49/16.37                                 (((setminusER) =>
% 122.49/16.37                                   (((setminusSubset2) =>
% 122.49/16.37                                     (((setminusERneg) =>
% 122.49/16.37                                       (((setminusELneg) =>
% 122.49/16.37                                         (((setminusILneg) =>
% 122.49/16.37                                           (((setminusIRneg) =>
% 122.49/16.37                                             (((setminusLsub) =>
% 122.49/16.37                                               (((setminusSubset1) =>
% 122.49/16.37                                                 (((symdiffE) =>
% 122.49/16.37                                                   (((symdiffI1) =>
% 122.49/16.37                                                     (((symdiffI2) =>
% 122.49/16.37                                                       (((symdiffIneg1) =>
% 122.49/16.37                                                         (((symdiffIneg2) =>
% 122.49/16.37                                                           (((secondinupair) =>
% 122.49/16.37                                                             (((setukpairIL) =>
% 122.49/16.37                                                               (((setukpairIR) =>
% 122.49/16.37                                                                 (((kpairiskpair) =>
% 122.49/16.37                                                                   (((kpairp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowerset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairset2E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairsubunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairinpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionE2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsuniq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR11) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR12) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairequniteq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemEL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempaircEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrSub) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrERa) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcImageSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (apProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (app) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (infuncsetfunc) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcinfuncset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcextLem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2lamEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theeq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrue) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueorfalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setminusT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setextT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subsetTI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTELcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTERcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTnotintersectT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementImpComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contraSubsetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTcontraSubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTILcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTIRcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTEcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule0) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_5) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1SetBreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (choice2fnsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compEex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionEcases) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionCommutes) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2W) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2A) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2B) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Equiv) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncInj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (leftInvIsSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjCantorThm) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (foundation2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSclos) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peano0notS) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peanoSinj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ordinalMinLem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (!!) @ (
% 122.49/16.37                                                                     ^[Y0 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (ordinal @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y1 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y2 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y2 @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ 
% 122.49/16.37                                                                      Y2) =>
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.37      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl957])).
% 122.49/16.37  thf(zip_derived_cl971, plain,
% 122.49/16.37      (~ (((binintersectLsub) =>
% 122.49/16.37           (((binintersectSubset2) =>
% 122.49/16.37             (((binintersectSubset3) =>
% 122.49/16.37               (((binintersectER) =>
% 122.49/16.37                 (((disjointsetsI1) =>
% 122.49/16.37                   (((binintersectRsub) =>
% 122.49/16.37                     (((binintersectSubset4) =>
% 122.49/16.37                       (((binintersectSubset1) =>
% 122.49/16.37                         (((bs114d) =>
% 122.49/16.37                           (((setminusI) =>
% 122.49/16.37                             (((setminusEL) =>
% 122.49/16.37                               (((setminusER) =>
% 122.49/16.37                                 (((setminusSubset2) =>
% 122.49/16.37                                   (((setminusERneg) =>
% 122.49/16.37                                     (((setminusELneg) =>
% 122.49/16.37                                       (((setminusILneg) =>
% 122.49/16.37                                         (((setminusIRneg) =>
% 122.49/16.37                                           (((setminusLsub) =>
% 122.49/16.37                                             (((setminusSubset1) =>
% 122.49/16.37                                               (((symdiffE) =>
% 122.49/16.37                                                 (((symdiffI1) =>
% 122.49/16.37                                                   (((symdiffI2) =>
% 122.49/16.37                                                     (((symdiffIneg1) =>
% 122.49/16.37                                                       (((symdiffIneg2) =>
% 122.49/16.37                                                         (((secondinupair) =>
% 122.49/16.37                                                           (((setukpairIL) =>
% 122.49/16.37                                                             (((setukpairIR) =>
% 122.49/16.37                                                               (((kpairiskpair) =>
% 122.49/16.37                                                                 (((kpairp) =>
% 122.49/16.37                                                                   (((singletonsubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowerset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairset2E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairsubunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairinpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionE2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsuniq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR11) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR12) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairequniteq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemEL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempaircEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrSub) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrERa) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcImageSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (apProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (app) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (infuncsetfunc) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcinfuncset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcextLem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2lamEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theeq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrue) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueorfalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setminusT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setextT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subsetTI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTELcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTERcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTnotintersectT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementImpComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contraSubsetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTcontraSubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTILcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTIRcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTEcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule0) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_5) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1SetBreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (choice2fnsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compEex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionEcases) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionCommutes) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2W) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2A) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2B) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Equiv) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncInj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (leftInvIsSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjCantorThm) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (foundation2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSclos) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peano0notS) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peanoSinj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ordinalMinLem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (!!) @ (
% 122.49/16.37                                                                     ^[Y0 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (ordinal @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y1 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y2 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y2 @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ 
% 122.49/16.37                                                                      Y2) =>
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.37      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl964])).
% 122.49/16.37  thf(zip_derived_cl978, plain,
% 122.49/16.37      (~ (((binintersectSubset2) =>
% 122.49/16.37           (((binintersectSubset3) =>
% 122.49/16.37             (((binintersectER) =>
% 122.49/16.37               (((disjointsetsI1) =>
% 122.49/16.37                 (((binintersectRsub) =>
% 122.49/16.37                   (((binintersectSubset4) =>
% 122.49/16.37                     (((binintersectSubset1) =>
% 122.49/16.37                       (((bs114d) =>
% 122.49/16.37                         (((setminusI) =>
% 122.49/16.37                           (((setminusEL) =>
% 122.49/16.37                             (((setminusER) =>
% 122.49/16.37                               (((setminusSubset2) =>
% 122.49/16.37                                 (((setminusERneg) =>
% 122.49/16.37                                   (((setminusELneg) =>
% 122.49/16.37                                     (((setminusILneg) =>
% 122.49/16.37                                       (((setminusIRneg) =>
% 122.49/16.37                                         (((setminusLsub) =>
% 122.49/16.37                                           (((setminusSubset1) =>
% 122.49/16.37                                             (((symdiffE) =>
% 122.49/16.37                                               (((symdiffI1) =>
% 122.49/16.37                                                 (((symdiffI2) =>
% 122.49/16.37                                                   (((symdiffIneg1) =>
% 122.49/16.37                                                     (((symdiffIneg2) =>
% 122.49/16.37                                                       (((secondinupair) =>
% 122.49/16.37                                                         (((setukpairIL) =>
% 122.49/16.37                                                           (((setukpairIR) =>
% 122.49/16.37                                                             (((kpairiskpair) =>
% 122.49/16.37                                                               (((kpairp) =>
% 122.49/16.37                                                                 (((singletonsubset) =>
% 122.49/16.37                                                                   (((singletoninpowerset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletoninpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairset2E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairsubunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairinpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionE2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsuniq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR11) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR12) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairequniteq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemEL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempaircEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrSub) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrERa) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcImageSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (apProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (app) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (infuncsetfunc) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcinfuncset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcextLem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2lamEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theeq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrue) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueorfalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setminusT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setextT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subsetTI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTELcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTERcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTnotintersectT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementImpComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contraSubsetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTcontraSubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTILcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTIRcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTEcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule0) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_5) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1SetBreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (choice2fnsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compEex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionEcases) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionCommutes) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2W) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2A) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2B) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Equiv) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncInj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (leftInvIsSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjCantorThm) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (foundation2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSclos) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peano0notS) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peanoSinj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ordinalMinLem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (!!) @ (
% 122.49/16.37                                                                     ^[Y0 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (ordinal @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y1 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y2 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y2 @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ 
% 122.49/16.37                                                                      Y2) =>
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.37      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl971])).
% 122.49/16.37  thf(zip_derived_cl985, plain,
% 122.49/16.37      (~ (((binintersectSubset3) =>
% 122.49/16.37           (((binintersectER) =>
% 122.49/16.37             (((disjointsetsI1) =>
% 122.49/16.37               (((binintersectRsub) =>
% 122.49/16.37                 (((binintersectSubset4) =>
% 122.49/16.37                   (((binintersectSubset1) =>
% 122.49/16.37                     (((bs114d) =>
% 122.49/16.37                       (((setminusI) =>
% 122.49/16.37                         (((setminusEL) =>
% 122.49/16.37                           (((setminusER) =>
% 122.49/16.37                             (((setminusSubset2) =>
% 122.49/16.37                               (((setminusERneg) =>
% 122.49/16.37                                 (((setminusELneg) =>
% 122.49/16.37                                   (((setminusILneg) =>
% 122.49/16.37                                     (((setminusIRneg) =>
% 122.49/16.37                                       (((setminusLsub) =>
% 122.49/16.37                                         (((setminusSubset1) =>
% 122.49/16.37                                           (((symdiffE) =>
% 122.49/16.37                                             (((symdiffI1) =>
% 122.49/16.37                                               (((symdiffI2) =>
% 122.49/16.37                                                 (((symdiffIneg1) =>
% 122.49/16.37                                                   (((symdiffIneg2) =>
% 122.49/16.37                                                     (((secondinupair) =>
% 122.49/16.37                                                       (((setukpairIL) =>
% 122.49/16.37                                                         (((setukpairIR) =>
% 122.49/16.37                                                           (((kpairiskpair) =>
% 122.49/16.37                                                             (((kpairp) =>
% 122.49/16.37                                                               (((singletonsubset) =>
% 122.49/16.37                                                                 (((singletoninpowerset) =>
% 122.49/16.37                                                                   (((singletoninpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairset2E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairsubunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairinpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionE2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsuniq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR11) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR12) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairequniteq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemEL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempaircEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrSub) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrERa) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcImageSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (apProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (app) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (infuncsetfunc) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcinfuncset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcextLem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2lamEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theeq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrue) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueorfalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setminusT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setextT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subsetTI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTELcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTERcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTnotintersectT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementImpComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contraSubsetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTcontraSubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTILcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTIRcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTEcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule0) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_5) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1SetBreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (choice2fnsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compEex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionEcases) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionCommutes) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2W) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2A) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2B) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Equiv) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncInj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (leftInvIsSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjCantorThm) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (foundation2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSclos) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peano0notS) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peanoSinj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ordinalMinLem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (!!) @ (
% 122.49/16.37                                                                     ^[Y0 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (ordinal @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y1 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y2 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y2 @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ 
% 122.49/16.37                                                                      Y2) =>
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.37      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl978])).
% 122.49/16.37  thf(zip_derived_cl994, plain,
% 122.49/16.37      (~ (((binintersectER) =>
% 122.49/16.37           (((disjointsetsI1) =>
% 122.49/16.37             (((binintersectRsub) =>
% 122.49/16.37               (((binintersectSubset4) =>
% 122.49/16.37                 (((binintersectSubset1) =>
% 122.49/16.37                   (((bs114d) =>
% 122.49/16.37                     (((setminusI) =>
% 122.49/16.37                       (((setminusEL) =>
% 122.49/16.37                         (((setminusER) =>
% 122.49/16.37                           (((setminusSubset2) =>
% 122.49/16.37                             (((setminusERneg) =>
% 122.49/16.37                               (((setminusELneg) =>
% 122.49/16.37                                 (((setminusILneg) =>
% 122.49/16.37                                   (((setminusIRneg) =>
% 122.49/16.37                                     (((setminusLsub) =>
% 122.49/16.37                                       (((setminusSubset1) =>
% 122.49/16.37                                         (((symdiffE) =>
% 122.49/16.37                                           (((symdiffI1) =>
% 122.49/16.37                                             (((symdiffI2) =>
% 122.49/16.37                                               (((symdiffIneg1) =>
% 122.49/16.37                                                 (((symdiffIneg2) =>
% 122.49/16.37                                                   (((secondinupair) =>
% 122.49/16.37                                                     (((setukpairIL) =>
% 122.49/16.37                                                       (((setukpairIR) =>
% 122.49/16.37                                                         (((kpairiskpair) =>
% 122.49/16.37                                                           (((kpairp) =>
% 122.49/16.37                                                             (((singletonsubset) =>
% 122.49/16.37                                                               (((singletoninpowerset) =>
% 122.49/16.37                                                                 (((singletoninpowunion) =>
% 122.49/16.37                                                                   (((upairset2E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairsubunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairinpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionE2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsuniq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR11) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR12) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairequniteq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemEL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempaircEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrSub) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrERa) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcImageSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (apProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (app) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (infuncsetfunc) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcinfuncset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcextLem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2lamEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theeq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrue) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueorfalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setminusT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setextT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subsetTI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTELcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTERcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTnotintersectT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementImpComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contraSubsetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTcontraSubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTILcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTIRcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTEcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule0) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_5) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1SetBreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (choice2fnsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compEex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionEcases) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionCommutes) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2W) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2A) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2B) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Equiv) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncInj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (leftInvIsSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjCantorThm) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (foundation2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSclos) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peano0notS) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peanoSinj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ordinalMinLem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (!!) @ (
% 122.49/16.37                                                                     ^[Y0 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (ordinal @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y1 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y2 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y2 @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ 
% 122.49/16.37                                                                      Y2) =>
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.37      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl985])).
% 122.49/16.37  thf(zip_derived_cl1002, plain,
% 122.49/16.37      (~ (((disjointsetsI1) =>
% 122.49/16.37           (((binintersectRsub) =>
% 122.49/16.37             (((binintersectSubset4) =>
% 122.49/16.37               (((binintersectSubset1) =>
% 122.49/16.37                 (((bs114d) =>
% 122.49/16.37                   (((setminusI) =>
% 122.49/16.37                     (((setminusEL) =>
% 122.49/16.37                       (((setminusER) =>
% 122.49/16.37                         (((setminusSubset2) =>
% 122.49/16.37                           (((setminusERneg) =>
% 122.49/16.37                             (((setminusELneg) =>
% 122.49/16.37                               (((setminusILneg) =>
% 122.49/16.37                                 (((setminusIRneg) =>
% 122.49/16.37                                   (((setminusLsub) =>
% 122.49/16.37                                     (((setminusSubset1) =>
% 122.49/16.37                                       (((symdiffE) =>
% 122.49/16.37                                         (((symdiffI1) =>
% 122.49/16.37                                           (((symdiffI2) =>
% 122.49/16.37                                             (((symdiffIneg1) =>
% 122.49/16.37                                               (((symdiffIneg2) =>
% 122.49/16.37                                                 (((secondinupair) =>
% 122.49/16.37                                                   (((setukpairIL) =>
% 122.49/16.37                                                     (((setukpairIR) =>
% 122.49/16.37                                                       (((kpairiskpair) =>
% 122.49/16.37                                                         (((kpairp) =>
% 122.49/16.37                                                           (((singletonsubset) =>
% 122.49/16.37                                                             (((singletoninpowerset) =>
% 122.49/16.37                                                               (((singletoninpowunion) =>
% 122.49/16.37                                                                 (((upairset2E) =>
% 122.49/16.37                                                                   (((upairsubunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairinpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionE2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsuniq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR11) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR12) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairequniteq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemEL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempaircEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrSub) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrERa) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcImageSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (apProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (app) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (infuncsetfunc) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcinfuncset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcextLem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2lamEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theeq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrue) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueorfalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setminusT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setextT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subsetTI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTELcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTERcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTnotintersectT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementImpComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contraSubsetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTcontraSubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTILcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTIRcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTEcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule0) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_5) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1SetBreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (choice2fnsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compEex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionEcases) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionCommutes) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2W) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2A) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2B) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Equiv) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncInj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (leftInvIsSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjCantorThm) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (foundation2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSclos) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peano0notS) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peanoSinj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ordinalMinLem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (!!) @ (
% 122.49/16.37                                                                     ^[Y0 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (ordinal @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y1 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y2 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y2 @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ 
% 122.49/16.37                                                                      Y2) =>
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.37      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl994])).
% 122.49/16.37  thf(zip_derived_cl1008, plain,
% 122.49/16.37      (~ (((binintersectRsub) =>
% 122.49/16.37           (((binintersectSubset4) =>
% 122.49/16.37             (((binintersectSubset1) =>
% 122.49/16.37               (((bs114d) =>
% 122.49/16.37                 (((setminusI) =>
% 122.49/16.37                   (((setminusEL) =>
% 122.49/16.37                     (((setminusER) =>
% 122.49/16.37                       (((setminusSubset2) =>
% 122.49/16.37                         (((setminusERneg) =>
% 122.49/16.37                           (((setminusELneg) =>
% 122.49/16.37                             (((setminusILneg) =>
% 122.49/16.37                               (((setminusIRneg) =>
% 122.49/16.37                                 (((setminusLsub) =>
% 122.49/16.37                                   (((setminusSubset1) =>
% 122.49/16.37                                     (((symdiffE) =>
% 122.49/16.37                                       (((symdiffI1) =>
% 122.49/16.37                                         (((symdiffI2) =>
% 122.49/16.37                                           (((symdiffIneg1) =>
% 122.49/16.37                                             (((symdiffIneg2) =>
% 122.49/16.37                                               (((secondinupair) =>
% 122.49/16.37                                                 (((setukpairIL) =>
% 122.49/16.37                                                   (((setukpairIR) =>
% 122.49/16.37                                                     (((kpairiskpair) =>
% 122.49/16.37                                                       (((kpairp) =>
% 122.49/16.37                                                         (((singletonsubset) =>
% 122.49/16.37                                                           (((singletoninpowerset) =>
% 122.49/16.37                                                             (((singletoninpowunion) =>
% 122.49/16.37                                                               (((upairset2E) =>
% 122.49/16.37                                                                 (((upairsubunion) =>
% 122.49/16.37                                                                   (((upairinpowunion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ubforcartprodlem3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempair) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionE2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1I2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (singletonsuniq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR11) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR12) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (upairequniteq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setukpairinjR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ksndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (kpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndin) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemEL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairmemER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodmempaircEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodfstpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodsndpairEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (cartprodpairsurjEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrSub) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrERa) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrEL2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (dpsetconstrER) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcImageSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (apProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (app) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (infuncsetfunc) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcinfuncset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamProp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lamp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2p) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (brelnall2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ex1E2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcextLem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcGraphProp4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (funcext2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ap2apEq2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (lam2lamEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (beta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eta2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalseProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueProp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifSingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ifp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (theeq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrue) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iffalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (iftrueorfalse) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setminusT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementT_lem) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setextT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subsetTI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (powersetTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTELcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintersectTERcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contrasubsetT3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementI1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementE1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementSub2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (doubleComplementEq) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTnotintersectT) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementImpComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (contraSubsetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementTcontraSubset) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTILcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTIRcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binunionTEcontra) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2a) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2b) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (demorgan2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule0) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz13rule4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_3) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_4) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz1_5) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1SetBreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (choice2fnsingleton) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1all1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (subbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (eqbreln1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1invE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1compEex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionprop) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIL) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionIR) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionI) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionE) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionEcases) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (breln1unionCommutes) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2W) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2A) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (woz2B) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Ex1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1Equiv) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1E) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (image1I) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (injFuncSetFuncInj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (leftInvIsSurj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (surjCantorThm) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (foundation2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (notinself2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSp) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (omegaSclos) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peano0notS) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (peanoSinj) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (binintTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (transitivesetOp2) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (setunionTransitive) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (ordinalMinLem1) =>
% 122.49/16.37                                                                     ((
% 122.49/16.37                                                                     (!!) @ (
% 122.49/16.37                                                                     ^[Y0 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (ordinal @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y1 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (!!) @ (
% 122.49/16.37                                                                      ^[Y2 : $i]:
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y2 @ 
% 122.49/16.37                                                                      Y0) =>
% 122.49/16.37                                                                      ((
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ 
% 122.49/16.37                                                                      Y2) =>
% 122.49/16.37                                                                      (in @ 
% 122.49/16.37                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.37      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1002])).
% 122.49/16.37  thf(zip_derived_cl1014, plain,
% 122.49/16.37      (~ (((binintersectSubset4) =>
% 122.49/16.37           (((binintersectSubset1) =>
% 122.49/16.37             (((bs114d) =>
% 122.49/16.37               (((setminusI) =>
% 122.49/16.37                 (((setminusEL) =>
% 122.49/16.37                   (((setminusER) =>
% 122.49/16.37                     (((setminusSubset2) =>
% 122.49/16.37                       (((setminusERneg) =>
% 122.49/16.37                         (((setminusELneg) =>
% 122.49/16.37                           (((setminusILneg) =>
% 122.49/16.37                             (((setminusIRneg) =>
% 122.49/16.37                               (((setminusLsub) =>
% 122.49/16.37                                 (((setminusSubset1) =>
% 122.49/16.37                                   (((symdiffE) =>
% 122.49/16.37                                     (((symdiffI1) =>
% 122.49/16.37                                       (((symdiffI2) =>
% 122.49/16.37                                         (((symdiffIneg1) =>
% 122.49/16.37                                           (((symdiffIneg2) =>
% 122.49/16.37                                             (((secondinupair) =>
% 122.49/16.37                                               (((setukpairIL) =>
% 122.49/16.37                                                 (((setukpairIR) =>
% 122.49/16.37                                                   (((kpairiskpair) =>
% 122.49/16.38                                                     (((kpairp) =>
% 122.49/16.38                                                       (((singletonsubset) =>
% 122.49/16.38                                                         (((singletoninpowerset) =>
% 122.49/16.38                                                           (((singletoninpowunion) =>
% 122.49/16.38                                                             (((upairset2E) =>
% 122.49/16.38                                                               (((upairsubunion) =>
% 122.49/16.38                                                                 (((upairinpowunion) =>
% 122.49/16.38                                                                   (((ubforcartprodlem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ubforcartprodlem2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ubforcartprodlem3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempair1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempair) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionE2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTEcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule0) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_5) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1SetBreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (choice2fnsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compEex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionEcases) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionCommutes) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2W) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2A) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2B) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Equiv) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1E) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncInj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (leftInvIsSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjCantorThm) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (foundation2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSclos) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peano0notS) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peanoSinj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ordinalMinLem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (!!) @ (
% 122.49/16.38                                                                     ^[Y0 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (ordinal @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y1 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y2 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y2 @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ 
% 122.49/16.38                                                                      Y2) =>
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.38      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1008])).
% 122.49/16.38  thf(zip_derived_cl1021, plain,
% 122.49/16.38      (~ (((binintersectSubset1) =>
% 122.49/16.38           (((bs114d) =>
% 122.49/16.38             (((setminusI) =>
% 122.49/16.38               (((setminusEL) =>
% 122.49/16.38                 (((setminusER) =>
% 122.49/16.38                   (((setminusSubset2) =>
% 122.49/16.38                     (((setminusERneg) =>
% 122.49/16.38                       (((setminusELneg) =>
% 122.49/16.38                         (((setminusILneg) =>
% 122.49/16.38                           (((setminusIRneg) =>
% 122.49/16.38                             (((setminusLsub) =>
% 122.49/16.38                               (((setminusSubset1) =>
% 122.49/16.38                                 (((symdiffE) =>
% 122.49/16.38                                   (((symdiffI1) =>
% 122.49/16.38                                     (((symdiffI2) =>
% 122.49/16.38                                       (((symdiffIneg1) =>
% 122.49/16.38                                         (((symdiffIneg2) =>
% 122.49/16.38                                           (((secondinupair) =>
% 122.49/16.38                                             (((setukpairIL) =>
% 122.49/16.38                                               (((setukpairIR) =>
% 122.49/16.38                                                 (((kpairiskpair) =>
% 122.49/16.38                                                   (((kpairp) =>
% 122.49/16.38                                                     (((singletonsubset) =>
% 122.49/16.38                                                       (((singletoninpowerset) =>
% 122.49/16.38                                                         (((singletoninpowunion) =>
% 122.49/16.38                                                           (((upairset2E) =>
% 122.49/16.38                                                             (((upairsubunion) =>
% 122.49/16.38                                                               (((upairinpowunion) =>
% 122.49/16.38                                                                 (((ubforcartprodlem1) =>
% 122.49/16.38                                                                   (((ubforcartprodlem2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ubforcartprodlem3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempair1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempair) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionE2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTEcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule0) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_5) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1SetBreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (choice2fnsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compEex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionEcases) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionCommutes) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2W) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2A) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2B) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Equiv) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1E) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncInj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (leftInvIsSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjCantorThm) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (foundation2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSclos) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peano0notS) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peanoSinj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ordinalMinLem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (!!) @ (
% 122.49/16.38                                                                     ^[Y0 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (ordinal @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y1 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y2 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y2 @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ 
% 122.49/16.38                                                                      Y2) =>
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.38      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1014])).
% 122.49/16.38  thf(zip_derived_cl1028, plain,
% 122.49/16.38      (~ (((bs114d) =>
% 122.49/16.38           (((setminusI) =>
% 122.49/16.38             (((setminusEL) =>
% 122.49/16.38               (((setminusER) =>
% 122.49/16.38                 (((setminusSubset2) =>
% 122.49/16.38                   (((setminusERneg) =>
% 122.49/16.38                     (((setminusELneg) =>
% 122.49/16.38                       (((setminusILneg) =>
% 122.49/16.38                         (((setminusIRneg) =>
% 122.49/16.38                           (((setminusLsub) =>
% 122.49/16.38                             (((setminusSubset1) =>
% 122.49/16.38                               (((symdiffE) =>
% 122.49/16.38                                 (((symdiffI1) =>
% 122.49/16.38                                   (((symdiffI2) =>
% 122.49/16.38                                     (((symdiffIneg1) =>
% 122.49/16.38                                       (((symdiffIneg2) =>
% 122.49/16.38                                         (((secondinupair) =>
% 122.49/16.38                                           (((setukpairIL) =>
% 122.49/16.38                                             (((setukpairIR) =>
% 122.49/16.38                                               (((kpairiskpair) =>
% 122.49/16.38                                                 (((kpairp) =>
% 122.49/16.38                                                   (((singletonsubset) =>
% 122.49/16.38                                                     (((singletoninpowerset) =>
% 122.49/16.38                                                       (((singletoninpowunion) =>
% 122.49/16.38                                                         (((upairset2E) =>
% 122.49/16.38                                                           (((upairsubunion) =>
% 122.49/16.38                                                             (((upairinpowunion) =>
% 122.49/16.38                                                               (((ubforcartprodlem1) =>
% 122.49/16.38                                                                 (((ubforcartprodlem2) =>
% 122.49/16.38                                                                   (((ubforcartprodlem3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempair1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempair) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionE2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTEcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule0) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_5) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1SetBreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (choice2fnsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compEex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionEcases) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionCommutes) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2W) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2A) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2B) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Equiv) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1E) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncInj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (leftInvIsSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjCantorThm) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (foundation2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSclos) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peano0notS) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peanoSinj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ordinalMinLem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (!!) @ (
% 122.49/16.38                                                                     ^[Y0 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (ordinal @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y1 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y2 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y2 @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ 
% 122.49/16.38                                                                      Y2) =>
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.38      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1021])).
% 122.49/16.38  thf(zip_derived_cl1034, plain,
% 122.49/16.38      (~ (((setminusI) =>
% 122.49/16.38           (((setminusEL) =>
% 122.49/16.38             (((setminusER) =>
% 122.49/16.38               (((setminusSubset2) =>
% 122.49/16.38                 (((setminusERneg) =>
% 122.49/16.38                   (((setminusELneg) =>
% 122.49/16.38                     (((setminusILneg) =>
% 122.49/16.38                       (((setminusIRneg) =>
% 122.49/16.38                         (((setminusLsub) =>
% 122.49/16.38                           (((setminusSubset1) =>
% 122.49/16.38                             (((symdiffE) =>
% 122.49/16.38                               (((symdiffI1) =>
% 122.49/16.38                                 (((symdiffI2) =>
% 122.49/16.38                                   (((symdiffIneg1) =>
% 122.49/16.38                                     (((symdiffIneg2) =>
% 122.49/16.38                                       (((secondinupair) =>
% 122.49/16.38                                         (((setukpairIL) =>
% 122.49/16.38                                           (((setukpairIR) =>
% 122.49/16.38                                             (((kpairiskpair) =>
% 122.49/16.38                                               (((kpairp) =>
% 122.49/16.38                                                 (((singletonsubset) =>
% 122.49/16.38                                                   (((singletoninpowerset) =>
% 122.49/16.38                                                     (((singletoninpowunion) =>
% 122.49/16.38                                                       (((upairset2E) =>
% 122.49/16.38                                                         (((upairsubunion) =>
% 122.49/16.38                                                           (((upairinpowunion) =>
% 122.49/16.38                                                             (((ubforcartprodlem1) =>
% 122.49/16.38                                                               (((ubforcartprodlem2) =>
% 122.49/16.38                                                                 (((ubforcartprodlem3) =>
% 122.49/16.38                                                                   (((cartprodpairin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempair1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempair) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionE2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTEcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule0) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_5) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1SetBreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (choice2fnsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compEex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionEcases) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionCommutes) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2W) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2A) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2B) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Equiv) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1E) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncInj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (leftInvIsSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjCantorThm) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (foundation2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSclos) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peano0notS) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peanoSinj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ordinalMinLem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (!!) @ (
% 122.49/16.38                                                                     ^[Y0 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (ordinal @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y1 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y2 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y2 @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ 
% 122.49/16.38                                                                      Y2) =>
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.38      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1028])).
% 122.49/16.38  thf(zip_derived_cl1041, plain,
% 122.49/16.38      (~ (((setminusEL) =>
% 122.49/16.38           (((setminusER) =>
% 122.49/16.38             (((setminusSubset2) =>
% 122.49/16.38               (((setminusERneg) =>
% 122.49/16.38                 (((setminusELneg) =>
% 122.49/16.38                   (((setminusILneg) =>
% 122.49/16.38                     (((setminusIRneg) =>
% 122.49/16.38                       (((setminusLsub) =>
% 122.49/16.38                         (((setminusSubset1) =>
% 122.49/16.38                           (((symdiffE) =>
% 122.49/16.38                             (((symdiffI1) =>
% 122.49/16.38                               (((symdiffI2) =>
% 122.49/16.38                                 (((symdiffIneg1) =>
% 122.49/16.38                                   (((symdiffIneg2) =>
% 122.49/16.38                                     (((secondinupair) =>
% 122.49/16.38                                       (((setukpairIL) =>
% 122.49/16.38                                         (((setukpairIR) =>
% 122.49/16.38                                           (((kpairiskpair) =>
% 122.49/16.38                                             (((kpairp) =>
% 122.49/16.38                                               (((singletonsubset) =>
% 122.49/16.38                                                 (((singletoninpowerset) =>
% 122.49/16.38                                                   (((singletoninpowunion) =>
% 122.49/16.38                                                     (((upairset2E) =>
% 122.49/16.38                                                       (((upairsubunion) =>
% 122.49/16.38                                                         (((upairinpowunion) =>
% 122.49/16.38                                                           (((ubforcartprodlem1) =>
% 122.49/16.38                                                             (((ubforcartprodlem2) =>
% 122.49/16.38                                                               (((ubforcartprodlem3) =>
% 122.49/16.38                                                                 (((cartprodpairin) =>
% 122.49/16.38                                                                   (((cartprodmempair1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempair) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionE2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTEcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule0) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_5) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1SetBreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (choice2fnsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compEex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionEcases) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionCommutes) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2W) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2A) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2B) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Equiv) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1E) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncInj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (leftInvIsSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjCantorThm) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (foundation2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSclos) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peano0notS) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peanoSinj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ordinalMinLem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (!!) @ (
% 122.49/16.38                                                                     ^[Y0 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (ordinal @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y1 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y2 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y2 @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ 
% 122.49/16.38                                                                      Y2) =>
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.38      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1034])).
% 122.49/16.38  thf(zip_derived_cl1047, plain,
% 122.49/16.38      (~ (((setminusER) =>
% 122.49/16.38           (((setminusSubset2) =>
% 122.49/16.38             (((setminusERneg) =>
% 122.49/16.38               (((setminusELneg) =>
% 122.49/16.38                 (((setminusILneg) =>
% 122.49/16.38                   (((setminusIRneg) =>
% 122.49/16.38                     (((setminusLsub) =>
% 122.49/16.38                       (((setminusSubset1) =>
% 122.49/16.38                         (((symdiffE) =>
% 122.49/16.38                           (((symdiffI1) =>
% 122.49/16.38                             (((symdiffI2) =>
% 122.49/16.38                               (((symdiffIneg1) =>
% 122.49/16.38                                 (((symdiffIneg2) =>
% 122.49/16.38                                   (((secondinupair) =>
% 122.49/16.38                                     (((setukpairIL) =>
% 122.49/16.38                                       (((setukpairIR) =>
% 122.49/16.38                                         (((kpairiskpair) =>
% 122.49/16.38                                           (((kpairp) =>
% 122.49/16.38                                             (((singletonsubset) =>
% 122.49/16.38                                               (((singletoninpowerset) =>
% 122.49/16.38                                                 (((singletoninpowunion) =>
% 122.49/16.38                                                   (((upairset2E) =>
% 122.49/16.38                                                     (((upairsubunion) =>
% 122.49/16.38                                                       (((upairinpowunion) =>
% 122.49/16.38                                                         (((ubforcartprodlem1) =>
% 122.49/16.38                                                           (((ubforcartprodlem2) =>
% 122.49/16.38                                                             (((ubforcartprodlem3) =>
% 122.49/16.38                                                               (((cartprodpairin) =>
% 122.49/16.38                                                                 (((cartprodmempair1) =>
% 122.49/16.38                                                                   (((cartprodmempair) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionE2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTEcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule0) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_5) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1SetBreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (choice2fnsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compEex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionEcases) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionCommutes) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2W) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2A) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2B) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Equiv) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1E) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncInj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (leftInvIsSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjCantorThm) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (foundation2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSclos) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peano0notS) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peanoSinj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ordinalMinLem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (!!) @ (
% 122.49/16.38                                                                     ^[Y0 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (ordinal @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y1 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y2 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y2 @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ 
% 122.49/16.38                                                                      Y2) =>
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.38      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1041])).
% 122.49/16.38  thf(zip_derived_cl1054, plain,
% 122.49/16.38      (~ (((setminusSubset2) =>
% 122.49/16.38           (((setminusERneg) =>
% 122.49/16.38             (((setminusELneg) =>
% 122.49/16.38               (((setminusILneg) =>
% 122.49/16.38                 (((setminusIRneg) =>
% 122.49/16.38                   (((setminusLsub) =>
% 122.49/16.38                     (((setminusSubset1) =>
% 122.49/16.38                       (((symdiffE) =>
% 122.49/16.38                         (((symdiffI1) =>
% 122.49/16.38                           (((symdiffI2) =>
% 122.49/16.38                             (((symdiffIneg1) =>
% 122.49/16.38                               (((symdiffIneg2) =>
% 122.49/16.38                                 (((secondinupair) =>
% 122.49/16.38                                   (((setukpairIL) =>
% 122.49/16.38                                     (((setukpairIR) =>
% 122.49/16.38                                       (((kpairiskpair) =>
% 122.49/16.38                                         (((kpairp) =>
% 122.49/16.38                                           (((singletonsubset) =>
% 122.49/16.38                                             (((singletoninpowerset) =>
% 122.49/16.38                                               (((singletoninpowunion) =>
% 122.49/16.38                                                 (((upairset2E) =>
% 122.49/16.38                                                   (((upairsubunion) =>
% 122.49/16.38                                                     (((upairinpowunion) =>
% 122.49/16.38                                                       (((ubforcartprodlem1) =>
% 122.49/16.38                                                         (((ubforcartprodlem2) =>
% 122.49/16.38                                                           (((ubforcartprodlem3) =>
% 122.49/16.38                                                             (((cartprodpairin) =>
% 122.49/16.38                                                               (((cartprodmempair1) =>
% 122.49/16.38                                                                 (((cartprodmempair) =>
% 122.49/16.38                                                                   (((setunionE2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTEcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule0) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_5) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1SetBreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (choice2fnsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compEex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionEcases) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionCommutes) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2W) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2A) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2B) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Equiv) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1E) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncInj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (leftInvIsSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjCantorThm) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (foundation2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSclos) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peano0notS) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peanoSinj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ordinalMinLem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (!!) @ (
% 122.49/16.38                                                                     ^[Y0 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (ordinal @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y1 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y2 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y2 @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ 
% 122.49/16.38                                                                      Y2) =>
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.38      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1047])).
% 122.49/16.38  thf(zip_derived_cl1061, plain,
% 122.49/16.38      (~ (((setminusERneg) =>
% 122.49/16.38           (((setminusELneg) =>
% 122.49/16.38             (((setminusILneg) =>
% 122.49/16.38               (((setminusIRneg) =>
% 122.49/16.38                 (((setminusLsub) =>
% 122.49/16.38                   (((setminusSubset1) =>
% 122.49/16.38                     (((symdiffE) =>
% 122.49/16.38                       (((symdiffI1) =>
% 122.49/16.38                         (((symdiffI2) =>
% 122.49/16.38                           (((symdiffIneg1) =>
% 122.49/16.38                             (((symdiffIneg2) =>
% 122.49/16.38                               (((secondinupair) =>
% 122.49/16.38                                 (((setukpairIL) =>
% 122.49/16.38                                   (((setukpairIR) =>
% 122.49/16.38                                     (((kpairiskpair) =>
% 122.49/16.38                                       (((kpairp) =>
% 122.49/16.38                                         (((singletonsubset) =>
% 122.49/16.38                                           (((singletoninpowerset) =>
% 122.49/16.38                                             (((singletoninpowunion) =>
% 122.49/16.38                                               (((upairset2E) =>
% 122.49/16.38                                                 (((upairsubunion) =>
% 122.49/16.38                                                   (((upairinpowunion) =>
% 122.49/16.38                                                     (((ubforcartprodlem1) =>
% 122.49/16.38                                                       (((ubforcartprodlem2) =>
% 122.49/16.38                                                         (((ubforcartprodlem3) =>
% 122.49/16.38                                                           (((cartprodpairin) =>
% 122.49/16.38                                                             (((cartprodmempair1) =>
% 122.49/16.38                                                               (((cartprodmempair) =>
% 122.49/16.38                                                                 (((setunionE2) =>
% 122.49/16.38                                                                   (((setunionsingleton1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTEcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule0) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_5) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1SetBreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (choice2fnsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compEex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionEcases) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionCommutes) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2W) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2A) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2B) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Equiv) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1E) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncInj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (leftInvIsSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjCantorThm) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (foundation2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSclos) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peano0notS) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peanoSinj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ordinalMinLem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (!!) @ (
% 122.49/16.38                                                                     ^[Y0 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (ordinal @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y1 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y2 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y2 @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ 
% 122.49/16.38                                                                      Y2) =>
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.38      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1054])).
% 122.49/16.38  thf(zip_derived_cl1068, plain,
% 122.49/16.38      (~ (((setminusELneg) =>
% 122.49/16.38           (((setminusILneg) =>
% 122.49/16.38             (((setminusIRneg) =>
% 122.49/16.38               (((setminusLsub) =>
% 122.49/16.38                 (((setminusSubset1) =>
% 122.49/16.38                   (((symdiffE) =>
% 122.49/16.38                     (((symdiffI1) =>
% 122.49/16.38                       (((symdiffI2) =>
% 122.49/16.38                         (((symdiffIneg1) =>
% 122.49/16.38                           (((symdiffIneg2) =>
% 122.49/16.38                             (((secondinupair) =>
% 122.49/16.38                               (((setukpairIL) =>
% 122.49/16.38                                 (((setukpairIR) =>
% 122.49/16.38                                   (((kpairiskpair) =>
% 122.49/16.38                                     (((kpairp) =>
% 122.49/16.38                                       (((singletonsubset) =>
% 122.49/16.38                                         (((singletoninpowerset) =>
% 122.49/16.38                                           (((singletoninpowunion) =>
% 122.49/16.38                                             (((upairset2E) =>
% 122.49/16.38                                               (((upairsubunion) =>
% 122.49/16.38                                                 (((upairinpowunion) =>
% 122.49/16.38                                                   (((ubforcartprodlem1) =>
% 122.49/16.38                                                     (((ubforcartprodlem2) =>
% 122.49/16.38                                                       (((ubforcartprodlem3) =>
% 122.49/16.38                                                         (((cartprodpairin) =>
% 122.49/16.38                                                           (((cartprodmempair1) =>
% 122.49/16.38                                                             (((cartprodmempair) =>
% 122.49/16.38                                                               (((setunionE2) =>
% 122.49/16.38                                                                 (((setunionsingleton1) =>
% 122.49/16.38                                                                   (((setunionsingleton2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTEcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule0) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_5) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1SetBreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (choice2fnsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compEex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionEcases) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionCommutes) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2W) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2A) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2B) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Equiv) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1E) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncInj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (leftInvIsSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjCantorThm) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (foundation2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSclos) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peano0notS) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peanoSinj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ordinalMinLem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (!!) @ (
% 122.49/16.38                                                                     ^[Y0 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (ordinal @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y1 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y2 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y2 @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ 
% 122.49/16.38                                                                      Y2) =>
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.38      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1061])).
% 122.49/16.38  thf(zip_derived_cl1075, plain,
% 122.49/16.38      (~ (((setminusILneg) =>
% 122.49/16.38           (((setminusIRneg) =>
% 122.49/16.38             (((setminusLsub) =>
% 122.49/16.38               (((setminusSubset1) =>
% 122.49/16.38                 (((symdiffE) =>
% 122.49/16.38                   (((symdiffI1) =>
% 122.49/16.38                     (((symdiffI2) =>
% 122.49/16.38                       (((symdiffIneg1) =>
% 122.49/16.38                         (((symdiffIneg2) =>
% 122.49/16.38                           (((secondinupair) =>
% 122.49/16.38                             (((setukpairIL) =>
% 122.49/16.38                               (((setukpairIR) =>
% 122.49/16.38                                 (((kpairiskpair) =>
% 122.49/16.38                                   (((kpairp) =>
% 122.49/16.38                                     (((singletonsubset) =>
% 122.49/16.38                                       (((singletoninpowerset) =>
% 122.49/16.38                                         (((singletoninpowunion) =>
% 122.49/16.38                                           (((upairset2E) =>
% 122.49/16.38                                             (((upairsubunion) =>
% 122.49/16.38                                               (((upairinpowunion) =>
% 122.49/16.38                                                 (((ubforcartprodlem1) =>
% 122.49/16.38                                                   (((ubforcartprodlem2) =>
% 122.49/16.38                                                     (((ubforcartprodlem3) =>
% 122.49/16.38                                                       (((cartprodpairin) =>
% 122.49/16.38                                                         (((cartprodmempair1) =>
% 122.49/16.38                                                           (((cartprodmempair) =>
% 122.49/16.38                                                             (((setunionE2) =>
% 122.49/16.38                                                               (((setunionsingleton1) =>
% 122.49/16.38                                                                 (((setunionsingleton2) =>
% 122.49/16.38                                                                   (((setunionsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTEcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule0) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_5) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1SetBreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (choice2fnsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compEex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionEcases) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionCommutes) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2W) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2A) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2B) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Equiv) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1E) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncInj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (leftInvIsSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjCantorThm) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (foundation2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSclos) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peano0notS) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peanoSinj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ordinalMinLem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (!!) @ (
% 122.49/16.38                                                                     ^[Y0 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (ordinal @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y1 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y2 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y2 @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ 
% 122.49/16.38                                                                      Y2) =>
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.38      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1068])).
% 122.49/16.38  thf(zip_derived_cl1082, plain,
% 122.49/16.38      (~ (((setminusIRneg) =>
% 122.49/16.38           (((setminusLsub) =>
% 122.49/16.38             (((setminusSubset1) =>
% 122.49/16.38               (((symdiffE) =>
% 122.49/16.38                 (((symdiffI1) =>
% 122.49/16.38                   (((symdiffI2) =>
% 122.49/16.38                     (((symdiffIneg1) =>
% 122.49/16.38                       (((symdiffIneg2) =>
% 122.49/16.38                         (((secondinupair) =>
% 122.49/16.38                           (((setukpairIL) =>
% 122.49/16.38                             (((setukpairIR) =>
% 122.49/16.38                               (((kpairiskpair) =>
% 122.49/16.38                                 (((kpairp) =>
% 122.49/16.38                                   (((singletonsubset) =>
% 122.49/16.38                                     (((singletoninpowerset) =>
% 122.49/16.38                                       (((singletoninpowunion) =>
% 122.49/16.38                                         (((upairset2E) =>
% 122.49/16.38                                           (((upairsubunion) =>
% 122.49/16.38                                             (((upairinpowunion) =>
% 122.49/16.38                                               (((ubforcartprodlem1) =>
% 122.49/16.38                                                 (((ubforcartprodlem2) =>
% 122.49/16.38                                                   (((ubforcartprodlem3) =>
% 122.49/16.38                                                     (((cartprodpairin) =>
% 122.49/16.38                                                       (((cartprodmempair1) =>
% 122.49/16.38                                                         (((cartprodmempair) =>
% 122.49/16.38                                                           (((setunionE2) =>
% 122.49/16.38                                                             (((setunionsingleton1) =>
% 122.49/16.38                                                               (((setunionsingleton2) =>
% 122.49/16.38                                                                 (((setunionsingleton) =>
% 122.49/16.38                                                                   (((singletonprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTEcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule0) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_5) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1SetBreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (choice2fnsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compEex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionEcases) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionCommutes) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2W) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2A) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2B) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Equiv) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1E) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncInj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (leftInvIsSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjCantorThm) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (foundation2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSclos) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peano0notS) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peanoSinj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ordinalMinLem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (!!) @ (
% 122.49/16.38                                                                     ^[Y0 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (ordinal @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y1 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y2 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y2 @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ 
% 122.49/16.38                                                                      Y2) =>
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.38      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1075])).
% 122.49/16.38  thf(zip_derived_cl1089, plain,
% 122.49/16.38      (~ (((setminusLsub) =>
% 122.49/16.38           (((setminusSubset1) =>
% 122.49/16.38             (((symdiffE) =>
% 122.49/16.38               (((symdiffI1) =>
% 122.49/16.38                 (((symdiffI2) =>
% 122.49/16.38                   (((symdiffIneg1) =>
% 122.49/16.38                     (((symdiffIneg2) =>
% 122.49/16.38                       (((secondinupair) =>
% 122.49/16.38                         (((setukpairIL) =>
% 122.49/16.38                           (((setukpairIR) =>
% 122.49/16.38                             (((kpairiskpair) =>
% 122.49/16.38                               (((kpairp) =>
% 122.49/16.38                                 (((singletonsubset) =>
% 122.49/16.38                                   (((singletoninpowerset) =>
% 122.49/16.38                                     (((singletoninpowunion) =>
% 122.49/16.38                                       (((upairset2E) =>
% 122.49/16.38                                         (((upairsubunion) =>
% 122.49/16.38                                           (((upairinpowunion) =>
% 122.49/16.38                                             (((ubforcartprodlem1) =>
% 122.49/16.38                                               (((ubforcartprodlem2) =>
% 122.49/16.38                                                 (((ubforcartprodlem3) =>
% 122.49/16.38                                                   (((cartprodpairin) =>
% 122.49/16.38                                                     (((cartprodmempair1) =>
% 122.49/16.38                                                       (((cartprodmempair) =>
% 122.49/16.38                                                         (((setunionE2) =>
% 122.49/16.38                                                           (((setunionsingleton1) =>
% 122.49/16.38                                                             (((setunionsingleton2) =>
% 122.49/16.38                                                               (((setunionsingleton) =>
% 122.49/16.38                                                                 (((singletonprop) =>
% 122.49/16.38                                                                   (((ex1E1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTEcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2a) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2b) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (demorgan2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule0) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz13rule4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz1_5) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1SetBreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (choice2fnsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1all1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1invE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1compEex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionIR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionE) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionEcases) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (breln1unionCommutes) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2W) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2A) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (woz2B) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Ex1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1Equiv) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1E) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (image1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (injFuncSetFuncInj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (leftInvIsSurj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (surjCantorThm) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (foundation2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (notinself2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (omegaSclos) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peano0notS) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (peanoSinj) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (transitivesetOp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setunionTransitive) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ordinalMinLem1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (!!) @ (
% 122.49/16.38                                                                     ^[Y0 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (ordinal @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y1 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (!!) @ (
% 122.49/16.38                                                                      ^[Y2 : $i]:
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y2 @ 
% 122.49/16.38                                                                      Y0) =>
% 122.49/16.38                                                                      ((
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ 
% 122.49/16.38                                                                      Y2) =>
% 122.49/16.38                                                                      (in @ 
% 122.49/16.38                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.38      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1082])).
% 122.49/16.38  thf(zip_derived_cl1096, plain,
% 122.49/16.38      (~ (((setminusSubset1) =>
% 122.49/16.38           (((symdiffE) =>
% 122.49/16.38             (((symdiffI1) =>
% 122.49/16.38               (((symdiffI2) =>
% 122.49/16.38                 (((symdiffIneg1) =>
% 122.49/16.38                   (((symdiffIneg2) =>
% 122.49/16.38                     (((secondinupair) =>
% 122.49/16.38                       (((setukpairIL) =>
% 122.49/16.38                         (((setukpairIR) =>
% 122.49/16.38                           (((kpairiskpair) =>
% 122.49/16.38                             (((kpairp) =>
% 122.49/16.38                               (((singletonsubset) =>
% 122.49/16.38                                 (((singletoninpowerset) =>
% 122.49/16.38                                   (((singletoninpowunion) =>
% 122.49/16.38                                     (((upairset2E) =>
% 122.49/16.38                                       (((upairsubunion) =>
% 122.49/16.38                                         (((upairinpowunion) =>
% 122.49/16.38                                           (((ubforcartprodlem1) =>
% 122.49/16.38                                             (((ubforcartprodlem2) =>
% 122.49/16.38                                               (((ubforcartprodlem3) =>
% 122.49/16.38                                                 (((cartprodpairin) =>
% 122.49/16.38                                                   (((cartprodmempair1) =>
% 122.49/16.38                                                     (((cartprodmempair) =>
% 122.49/16.38                                                       (((setunionE2) =>
% 122.49/16.38                                                         (((setunionsingleton1) =>
% 122.49/16.38                                                           (((setunionsingleton2) =>
% 122.49/16.38                                                             (((setunionsingleton) =>
% 122.49/16.38                                                               (((singletonprop) =>
% 122.49/16.38                                                                 (((ex1E1) =>
% 122.49/16.38                                                                   (((ex1I) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1I2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (singletonsuniq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theprop) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR11) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR12) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (upairequniteq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setukpairinjR) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndsingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ksndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (kpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndin) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemEL) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairmemER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodmempaircEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodfstpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodsndpairEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (cartprodpairsurjEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrSub) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setOfPairsIsBReln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrERa) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrEL2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (dpsetconstrER) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcImageSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (apProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (app) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (infuncsetfunc) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcinfuncset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamProp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lamp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2p) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (brelnall2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ex1E2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcextLem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcGraphProp4) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eqbreln) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (funcext2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ap2apEq2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (lam2lamEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (beta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (eta2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalseProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueProp2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifSingleton) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (ifp) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (theeq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrue) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iffalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (iftrueorfalse) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setminusT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementT_lem) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (setextT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (subsetTI) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (powersetTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTELcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binintersectTERcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contrasubsetT3) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementI1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementE1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub1) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementSub2) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (doubleComplementEq) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTnotintersectT) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementImpComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (contraSubsetComplement) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (complementTcontraSubset) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTILcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.38                                                                     (binunionTIRcontra) =>
% 122.49/16.38                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1089])).
% 122.49/16.39  thf(zip_derived_cl1103, plain,
% 122.49/16.39      (~ (((symdiffE) =>
% 122.49/16.39           (((symdiffI1) =>
% 122.49/16.39             (((symdiffI2) =>
% 122.49/16.39               (((symdiffIneg1) =>
% 122.49/16.39                 (((symdiffIneg2) =>
% 122.49/16.39                   (((secondinupair) =>
% 122.49/16.39                     (((setukpairIL) =>
% 122.49/16.39                       (((setukpairIR) =>
% 122.49/16.39                         (((kpairiskpair) =>
% 122.49/16.39                           (((kpairp) =>
% 122.49/16.39                             (((singletonsubset) =>
% 122.49/16.39                               (((singletoninpowerset) =>
% 122.49/16.39                                 (((singletoninpowunion) =>
% 122.49/16.39                                   (((upairset2E) =>
% 122.49/16.39                                     (((upairsubunion) =>
% 122.49/16.39                                       (((upairinpowunion) =>
% 122.49/16.39                                         (((ubforcartprodlem1) =>
% 122.49/16.39                                           (((ubforcartprodlem2) =>
% 122.49/16.39                                             (((ubforcartprodlem3) =>
% 122.49/16.39                                               (((cartprodpairin) =>
% 122.49/16.39                                                 (((cartprodmempair1) =>
% 122.49/16.39                                                   (((cartprodmempair) =>
% 122.49/16.39                                                     (((setunionE2) =>
% 122.49/16.39                                                       (((setunionsingleton1) =>
% 122.49/16.39                                                         (((setunionsingleton2) =>
% 122.49/16.39                                                           (((setunionsingleton) =>
% 122.49/16.39                                                             (((singletonprop) =>
% 122.49/16.39                                                               (((ex1E1) =>
% 122.49/16.39                                                                 (((ex1I) =>
% 122.49/16.39                                                                   (((ex1I2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (singletonsuniq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kfstsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR11) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR12) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1096])).
% 122.49/16.39  thf(zip_derived_cl1111, plain,
% 122.49/16.39      (~ (((symdiffI1) =>
% 122.49/16.39           (((symdiffI2) =>
% 122.49/16.39             (((symdiffIneg1) =>
% 122.49/16.39               (((symdiffIneg2) =>
% 122.49/16.39                 (((secondinupair) =>
% 122.49/16.39                   (((setukpairIL) =>
% 122.49/16.39                     (((setukpairIR) =>
% 122.49/16.39                       (((kpairiskpair) =>
% 122.49/16.39                         (((kpairp) =>
% 122.49/16.39                           (((singletonsubset) =>
% 122.49/16.39                             (((singletoninpowerset) =>
% 122.49/16.39                               (((singletoninpowunion) =>
% 122.49/16.39                                 (((upairset2E) =>
% 122.49/16.39                                   (((upairsubunion) =>
% 122.49/16.39                                     (((upairinpowunion) =>
% 122.49/16.39                                       (((ubforcartprodlem1) =>
% 122.49/16.39                                         (((ubforcartprodlem2) =>
% 122.49/16.39                                           (((ubforcartprodlem3) =>
% 122.49/16.39                                             (((cartprodpairin) =>
% 122.49/16.39                                               (((cartprodmempair1) =>
% 122.49/16.39                                                 (((cartprodmempair) =>
% 122.49/16.39                                                   (((setunionE2) =>
% 122.49/16.39                                                     (((setunionsingleton1) =>
% 122.49/16.39                                                       (((setunionsingleton2) =>
% 122.49/16.39                                                         (((setunionsingleton) =>
% 122.49/16.39                                                           (((singletonprop) =>
% 122.49/16.39                                                             (((ex1E1) =>
% 122.49/16.39                                                               (((ex1I) =>
% 122.49/16.39                                                                 (((ex1I2) =>
% 122.49/16.39                                                                   (((singletonsuniq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kfstsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR11) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR12) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1103])).
% 122.49/16.39  thf(zip_derived_cl1119, plain,
% 122.49/16.39      (~ (((symdiffI2) =>
% 122.49/16.39           (((symdiffIneg1) =>
% 122.49/16.39             (((symdiffIneg2) =>
% 122.49/16.39               (((secondinupair) =>
% 122.49/16.39                 (((setukpairIL) =>
% 122.49/16.39                   (((setukpairIR) =>
% 122.49/16.39                     (((kpairiskpair) =>
% 122.49/16.39                       (((kpairp) =>
% 122.49/16.39                         (((singletonsubset) =>
% 122.49/16.39                           (((singletoninpowerset) =>
% 122.49/16.39                             (((singletoninpowunion) =>
% 122.49/16.39                               (((upairset2E) =>
% 122.49/16.39                                 (((upairsubunion) =>
% 122.49/16.39                                   (((upairinpowunion) =>
% 122.49/16.39                                     (((ubforcartprodlem1) =>
% 122.49/16.39                                       (((ubforcartprodlem2) =>
% 122.49/16.39                                         (((ubforcartprodlem3) =>
% 122.49/16.39                                           (((cartprodpairin) =>
% 122.49/16.39                                             (((cartprodmempair1) =>
% 122.49/16.39                                               (((cartprodmempair) =>
% 122.49/16.39                                                 (((setunionE2) =>
% 122.49/16.39                                                   (((setunionsingleton1) =>
% 122.49/16.39                                                     (((setunionsingleton2) =>
% 122.49/16.39                                                       (((setunionsingleton) =>
% 122.49/16.39                                                         (((singletonprop) =>
% 122.49/16.39                                                           (((ex1E1) =>
% 122.49/16.39                                                             (((ex1I) =>
% 122.49/16.39                                                               (((ex1I2) =>
% 122.49/16.39                                                                 (((singletonsuniq) =>
% 122.49/16.39                                                                   (((setukpairinjL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kfstsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR11) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR12) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1111])).
% 122.49/16.39  thf(zip_derived_cl1125, plain,
% 122.49/16.39      (~ (((symdiffIneg1) =>
% 122.49/16.39           (((symdiffIneg2) =>
% 122.49/16.39             (((secondinupair) =>
% 122.49/16.39               (((setukpairIL) =>
% 122.49/16.39                 (((setukpairIR) =>
% 122.49/16.39                   (((kpairiskpair) =>
% 122.49/16.39                     (((kpairp) =>
% 122.49/16.39                       (((singletonsubset) =>
% 122.49/16.39                         (((singletoninpowerset) =>
% 122.49/16.39                           (((singletoninpowunion) =>
% 122.49/16.39                             (((upairset2E) =>
% 122.49/16.39                               (((upairsubunion) =>
% 122.49/16.39                                 (((upairinpowunion) =>
% 122.49/16.39                                   (((ubforcartprodlem1) =>
% 122.49/16.39                                     (((ubforcartprodlem2) =>
% 122.49/16.39                                       (((ubforcartprodlem3) =>
% 122.49/16.39                                         (((cartprodpairin) =>
% 122.49/16.39                                           (((cartprodmempair1) =>
% 122.49/16.39                                             (((cartprodmempair) =>
% 122.49/16.39                                               (((setunionE2) =>
% 122.49/16.39                                                 (((setunionsingleton1) =>
% 122.49/16.39                                                   (((setunionsingleton2) =>
% 122.49/16.39                                                     (((setunionsingleton) =>
% 122.49/16.39                                                       (((singletonprop) =>
% 122.49/16.39                                                         (((ex1E1) =>
% 122.49/16.39                                                           (((ex1I) =>
% 122.49/16.39                                                             (((ex1I2) =>
% 122.49/16.39                                                               (((singletonsuniq) =>
% 122.49/16.39                                                                 (((setukpairinjL1) =>
% 122.49/16.39                                                                   (((kfstsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR11) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR12) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1119])).
% 122.49/16.39  thf(zip_derived_cl1131, plain,
% 122.49/16.39      (~ (((symdiffIneg2) =>
% 122.49/16.39           (((secondinupair) =>
% 122.49/16.39             (((setukpairIL) =>
% 122.49/16.39               (((setukpairIR) =>
% 122.49/16.39                 (((kpairiskpair) =>
% 122.49/16.39                   (((kpairp) =>
% 122.49/16.39                     (((singletonsubset) =>
% 122.49/16.39                       (((singletoninpowerset) =>
% 122.49/16.39                         (((singletoninpowunion) =>
% 122.49/16.39                           (((upairset2E) =>
% 122.49/16.39                             (((upairsubunion) =>
% 122.49/16.39                               (((upairinpowunion) =>
% 122.49/16.39                                 (((ubforcartprodlem1) =>
% 122.49/16.39                                   (((ubforcartprodlem2) =>
% 122.49/16.39                                     (((ubforcartprodlem3) =>
% 122.49/16.39                                       (((cartprodpairin) =>
% 122.49/16.39                                         (((cartprodmempair1) =>
% 122.49/16.39                                           (((cartprodmempair) =>
% 122.49/16.39                                             (((setunionE2) =>
% 122.49/16.39                                               (((setunionsingleton1) =>
% 122.49/16.39                                                 (((setunionsingleton2) =>
% 122.49/16.39                                                   (((setunionsingleton) =>
% 122.49/16.39                                                     (((singletonprop) =>
% 122.49/16.39                                                       (((ex1E1) =>
% 122.49/16.39                                                         (((ex1I) =>
% 122.49/16.39                                                           (((ex1I2) =>
% 122.49/16.39                                                             (((singletonsuniq) =>
% 122.49/16.39                                                               (((setukpairinjL1) =>
% 122.49/16.39                                                                 (((kfstsingleton) =>
% 122.49/16.39                                                                   (((theprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR11) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR12) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1125])).
% 122.49/16.39  thf(zip_derived_cl1138, plain,
% 122.49/16.39      (~ (((secondinupair) =>
% 122.49/16.39           (((setukpairIL) =>
% 122.49/16.39             (((setukpairIR) =>
% 122.49/16.39               (((kpairiskpair) =>
% 122.49/16.39                 (((kpairp) =>
% 122.49/16.39                   (((singletonsubset) =>
% 122.49/16.39                     (((singletoninpowerset) =>
% 122.49/16.39                       (((singletoninpowunion) =>
% 122.49/16.39                         (((upairset2E) =>
% 122.49/16.39                           (((upairsubunion) =>
% 122.49/16.39                             (((upairinpowunion) =>
% 122.49/16.39                               (((ubforcartprodlem1) =>
% 122.49/16.39                                 (((ubforcartprodlem2) =>
% 122.49/16.39                                   (((ubforcartprodlem3) =>
% 122.49/16.39                                     (((cartprodpairin) =>
% 122.49/16.39                                       (((cartprodmempair1) =>
% 122.49/16.39                                         (((cartprodmempair) =>
% 122.49/16.39                                           (((setunionE2) =>
% 122.49/16.39                                             (((setunionsingleton1) =>
% 122.49/16.39                                               (((setunionsingleton2) =>
% 122.49/16.39                                                 (((setunionsingleton) =>
% 122.49/16.39                                                   (((singletonprop) =>
% 122.49/16.39                                                     (((ex1E1) =>
% 122.49/16.39                                                       (((ex1I) =>
% 122.49/16.39                                                         (((ex1I2) =>
% 122.49/16.39                                                           (((singletonsuniq) =>
% 122.49/16.39                                                             (((setukpairinjL1) =>
% 122.49/16.39                                                               (((kfstsingleton) =>
% 122.49/16.39                                                                 (((theprop) =>
% 122.49/16.39                                                                   (((kfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR11) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR12) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1131])).
% 122.49/16.39  thf(zip_derived_cl1145, plain,
% 122.49/16.39      (~ (((setukpairIL) =>
% 122.49/16.39           (((setukpairIR) =>
% 122.49/16.39             (((kpairiskpair) =>
% 122.49/16.39               (((kpairp) =>
% 122.49/16.39                 (((singletonsubset) =>
% 122.49/16.39                   (((singletoninpowerset) =>
% 122.49/16.39                     (((singletoninpowunion) =>
% 122.49/16.39                       (((upairset2E) =>
% 122.49/16.39                         (((upairsubunion) =>
% 122.49/16.39                           (((upairinpowunion) =>
% 122.49/16.39                             (((ubforcartprodlem1) =>
% 122.49/16.39                               (((ubforcartprodlem2) =>
% 122.49/16.39                                 (((ubforcartprodlem3) =>
% 122.49/16.39                                   (((cartprodpairin) =>
% 122.49/16.39                                     (((cartprodmempair1) =>
% 122.49/16.39                                       (((cartprodmempair) =>
% 122.49/16.39                                         (((setunionE2) =>
% 122.49/16.39                                           (((setunionsingleton1) =>
% 122.49/16.39                                             (((setunionsingleton2) =>
% 122.49/16.39                                               (((setunionsingleton) =>
% 122.49/16.39                                                 (((singletonprop) =>
% 122.49/16.39                                                   (((ex1E1) =>
% 122.49/16.39                                                     (((ex1I) =>
% 122.49/16.39                                                       (((ex1I2) =>
% 122.49/16.39                                                         (((singletonsuniq) =>
% 122.49/16.39                                                           (((setukpairinjL1) =>
% 122.49/16.39                                                             (((kfstsingleton) =>
% 122.49/16.39                                                               (((theprop) =>
% 122.49/16.39                                                                 (((kfstpairEq) =>
% 122.49/16.39                                                                   (((cartprodfstin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR11) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR12) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1138])).
% 122.49/16.39  thf(zip_derived_cl1153, plain,
% 122.49/16.39      (~ (((setukpairIR) =>
% 122.49/16.39           (((kpairiskpair) =>
% 122.49/16.39             (((kpairp) =>
% 122.49/16.39               (((singletonsubset) =>
% 122.49/16.39                 (((singletoninpowerset) =>
% 122.49/16.39                   (((singletoninpowunion) =>
% 122.49/16.39                     (((upairset2E) =>
% 122.49/16.39                       (((upairsubunion) =>
% 122.49/16.39                         (((upairinpowunion) =>
% 122.49/16.39                           (((ubforcartprodlem1) =>
% 122.49/16.39                             (((ubforcartprodlem2) =>
% 122.49/16.39                               (((ubforcartprodlem3) =>
% 122.49/16.39                                 (((cartprodpairin) =>
% 122.49/16.39                                   (((cartprodmempair1) =>
% 122.49/16.39                                     (((cartprodmempair) =>
% 122.49/16.39                                       (((setunionE2) =>
% 122.49/16.39                                         (((setunionsingleton1) =>
% 122.49/16.39                                           (((setunionsingleton2) =>
% 122.49/16.39                                             (((setunionsingleton) =>
% 122.49/16.39                                               (((singletonprop) =>
% 122.49/16.39                                                 (((ex1E1) =>
% 122.49/16.39                                                   (((ex1I) =>
% 122.49/16.39                                                     (((ex1I2) =>
% 122.49/16.39                                                       (((singletonsuniq) =>
% 122.49/16.39                                                         (((setukpairinjL1) =>
% 122.49/16.39                                                           (((kfstsingleton) =>
% 122.49/16.39                                                             (((theprop) =>
% 122.49/16.39                                                               (((kfstpairEq) =>
% 122.49/16.39                                                                 (((cartprodfstin) =>
% 122.49/16.39                                                                   (((setukpairinjL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR11) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR12) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1145])).
% 122.49/16.39  thf(zip_derived_cl1162, plain,
% 122.49/16.39      (~ (((kpairiskpair) =>
% 122.49/16.39           (((kpairp) =>
% 122.49/16.39             (((singletonsubset) =>
% 122.49/16.39               (((singletoninpowerset) =>
% 122.49/16.39                 (((singletoninpowunion) =>
% 122.49/16.39                   (((upairset2E) =>
% 122.49/16.39                     (((upairsubunion) =>
% 122.49/16.39                       (((upairinpowunion) =>
% 122.49/16.39                         (((ubforcartprodlem1) =>
% 122.49/16.39                           (((ubforcartprodlem2) =>
% 122.49/16.39                             (((ubforcartprodlem3) =>
% 122.49/16.39                               (((cartprodpairin) =>
% 122.49/16.39                                 (((cartprodmempair1) =>
% 122.49/16.39                                   (((cartprodmempair) =>
% 122.49/16.39                                     (((setunionE2) =>
% 122.49/16.39                                       (((setunionsingleton1) =>
% 122.49/16.39                                         (((setunionsingleton2) =>
% 122.49/16.39                                           (((setunionsingleton) =>
% 122.49/16.39                                             (((singletonprop) =>
% 122.49/16.39                                               (((ex1E1) =>
% 122.49/16.39                                                 (((ex1I) =>
% 122.49/16.39                                                   (((ex1I2) =>
% 122.49/16.39                                                     (((singletonsuniq) =>
% 122.49/16.39                                                       (((setukpairinjL1) =>
% 122.49/16.39                                                         (((kfstsingleton) =>
% 122.49/16.39                                                           (((theprop) =>
% 122.49/16.39                                                             (((kfstpairEq) =>
% 122.49/16.39                                                               (((cartprodfstin) =>
% 122.49/16.39                                                                 (((setukpairinjL2) =>
% 122.49/16.39                                                                   (((setukpairinjL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR11) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR12) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1153])).
% 122.49/16.39  thf(zip_derived_cl1172, plain,
% 122.49/16.39      (~ (((kpairp) =>
% 122.49/16.39           (((singletonsubset) =>
% 122.49/16.39             (((singletoninpowerset) =>
% 122.49/16.39               (((singletoninpowunion) =>
% 122.49/16.39                 (((upairset2E) =>
% 122.49/16.39                   (((upairsubunion) =>
% 122.49/16.39                     (((upairinpowunion) =>
% 122.49/16.39                       (((ubforcartprodlem1) =>
% 122.49/16.39                         (((ubforcartprodlem2) =>
% 122.49/16.39                           (((ubforcartprodlem3) =>
% 122.49/16.39                             (((cartprodpairin) =>
% 122.49/16.39                               (((cartprodmempair1) =>
% 122.49/16.39                                 (((cartprodmempair) =>
% 122.49/16.39                                   (((setunionE2) =>
% 122.49/16.39                                     (((setunionsingleton1) =>
% 122.49/16.39                                       (((setunionsingleton2) =>
% 122.49/16.39                                         (((setunionsingleton) =>
% 122.49/16.39                                           (((singletonprop) =>
% 122.49/16.39                                             (((ex1E1) =>
% 122.49/16.39                                               (((ex1I) =>
% 122.49/16.39                                                 (((ex1I2) =>
% 122.49/16.39                                                   (((singletonsuniq) =>
% 122.49/16.39                                                     (((setukpairinjL1) =>
% 122.49/16.39                                                       (((kfstsingleton) =>
% 122.49/16.39                                                         (((theprop) =>
% 122.49/16.39                                                           (((kfstpairEq) =>
% 122.49/16.39                                                             (((cartprodfstin) =>
% 122.49/16.39                                                               (((setukpairinjL2) =>
% 122.49/16.39                                                                 (((setukpairinjL) =>
% 122.49/16.39                                                                   (((setukpairinjR11) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR12) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1162])).
% 122.49/16.39  thf(zip_derived_cl1185, plain,
% 122.49/16.39      (~ (((singletonsubset) =>
% 122.49/16.39           (((singletoninpowerset) =>
% 122.49/16.39             (((singletoninpowunion) =>
% 122.49/16.39               (((upairset2E) =>
% 122.49/16.39                 (((upairsubunion) =>
% 122.49/16.39                   (((upairinpowunion) =>
% 122.49/16.39                     (((ubforcartprodlem1) =>
% 122.49/16.39                       (((ubforcartprodlem2) =>
% 122.49/16.39                         (((ubforcartprodlem3) =>
% 122.49/16.39                           (((cartprodpairin) =>
% 122.49/16.39                             (((cartprodmempair1) =>
% 122.49/16.39                               (((cartprodmempair) =>
% 122.49/16.39                                 (((setunionE2) =>
% 122.49/16.39                                   (((setunionsingleton1) =>
% 122.49/16.39                                     (((setunionsingleton2) =>
% 122.49/16.39                                       (((setunionsingleton) =>
% 122.49/16.39                                         (((singletonprop) =>
% 122.49/16.39                                           (((ex1E1) =>
% 122.49/16.39                                             (((ex1I) =>
% 122.49/16.39                                               (((ex1I2) =>
% 122.49/16.39                                                 (((singletonsuniq) =>
% 122.49/16.39                                                   (((setukpairinjL1) =>
% 122.49/16.39                                                     (((kfstsingleton) =>
% 122.49/16.39                                                       (((theprop) =>
% 122.49/16.39                                                         (((kfstpairEq) =>
% 122.49/16.39                                                           (((cartprodfstin) =>
% 122.49/16.39                                                             (((setukpairinjL2) =>
% 122.49/16.39                                                               (((setukpairinjL) =>
% 122.49/16.39                                                                 (((setukpairinjR11) =>
% 122.49/16.39                                                                   (((setukpairinjR12) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1172])).
% 122.49/16.39  thf(zip_derived_cl1195, plain,
% 122.49/16.39      (~ (((singletoninpowerset) =>
% 122.49/16.39           (((singletoninpowunion) =>
% 122.49/16.39             (((upairset2E) =>
% 122.49/16.39               (((upairsubunion) =>
% 122.49/16.39                 (((upairinpowunion) =>
% 122.49/16.39                   (((ubforcartprodlem1) =>
% 122.49/16.39                     (((ubforcartprodlem2) =>
% 122.49/16.39                       (((ubforcartprodlem3) =>
% 122.49/16.39                         (((cartprodpairin) =>
% 122.49/16.39                           (((cartprodmempair1) =>
% 122.49/16.39                             (((cartprodmempair) =>
% 122.49/16.39                               (((setunionE2) =>
% 122.49/16.39                                 (((setunionsingleton1) =>
% 122.49/16.39                                   (((setunionsingleton2) =>
% 122.49/16.39                                     (((setunionsingleton) =>
% 122.49/16.39                                       (((singletonprop) =>
% 122.49/16.39                                         (((ex1E1) =>
% 122.49/16.39                                           (((ex1I) =>
% 122.49/16.39                                             (((ex1I2) =>
% 122.49/16.39                                               (((singletonsuniq) =>
% 122.49/16.39                                                 (((setukpairinjL1) =>
% 122.49/16.39                                                   (((kfstsingleton) =>
% 122.49/16.39                                                     (((theprop) =>
% 122.49/16.39                                                       (((kfstpairEq) =>
% 122.49/16.39                                                         (((cartprodfstin) =>
% 122.49/16.39                                                           (((setukpairinjL2) =>
% 122.49/16.39                                                             (((setukpairinjL) =>
% 122.49/16.39                                                               (((setukpairinjR11) =>
% 122.49/16.39                                                                 (((setukpairinjR12) =>
% 122.49/16.39                                                                   (((setukpairinjR1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setunionTransitive) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ordinalMinLem1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (!!) @ (
% 122.49/16.39                                                                     ^[Y0 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (ordinal @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y1 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (!!) @ (
% 122.49/16.39                                                                      ^[Y2 : $i]:
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y2 @ 
% 122.49/16.39                                                                      Y0) =>
% 122.49/16.39                                                                      ((
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ 
% 122.49/16.39                                                                      Y2) =>
% 122.49/16.39                                                                      (in @ 
% 122.49/16.39                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.39      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1185])).
% 122.49/16.39  thf(zip_derived_cl1202, plain,
% 122.49/16.39      (~ (((singletoninpowunion) =>
% 122.49/16.39           (((upairset2E) =>
% 122.49/16.39             (((upairsubunion) =>
% 122.49/16.39               (((upairinpowunion) =>
% 122.49/16.39                 (((ubforcartprodlem1) =>
% 122.49/16.39                   (((ubforcartprodlem2) =>
% 122.49/16.39                     (((ubforcartprodlem3) =>
% 122.49/16.39                       (((cartprodpairin) =>
% 122.49/16.39                         (((cartprodmempair1) =>
% 122.49/16.39                           (((cartprodmempair) =>
% 122.49/16.39                             (((setunionE2) =>
% 122.49/16.39                               (((setunionsingleton1) =>
% 122.49/16.39                                 (((setunionsingleton2) =>
% 122.49/16.39                                   (((setunionsingleton) =>
% 122.49/16.39                                     (((singletonprop) =>
% 122.49/16.39                                       (((ex1E1) =>
% 122.49/16.39                                         (((ex1I) =>
% 122.49/16.39                                           (((ex1I2) =>
% 122.49/16.39                                             (((singletonsuniq) =>
% 122.49/16.39                                               (((setukpairinjL1) =>
% 122.49/16.39                                                 (((kfstsingleton) =>
% 122.49/16.39                                                   (((theprop) =>
% 122.49/16.39                                                     (((kfstpairEq) =>
% 122.49/16.39                                                       (((cartprodfstin) =>
% 122.49/16.39                                                         (((setukpairinjL2) =>
% 122.49/16.39                                                           (((setukpairinjL) =>
% 122.49/16.39                                                             (((setukpairinjR11) =>
% 122.49/16.39                                                               (((setukpairinjR12) =>
% 122.49/16.39                                                                 (((setukpairinjR1) =>
% 122.49/16.39                                                                   (((upairequniteq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setukpairinjR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ksndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (kpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndin) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemEL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairmemER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodmempaircEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodfstpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodsndpairEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (cartprodpairsurjEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrSub) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrERa) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrEL2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (dpsetconstrER) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcImageSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (apProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (app) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (infuncsetfunc) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcinfuncset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamProp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lamp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2p) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (brelnall2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ex1E2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcextLem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcGraphProp4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (funcext2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ap2apEq2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (lam2lamEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (beta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eta2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalseProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueProp2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifSingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (ifp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (theeq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrue) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iffalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (iftrueorfalse) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setminusT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementT_lem) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setextT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subsetTI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (powersetTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTELcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binintersectTERcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contrasubsetT3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementI1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementE1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementSub2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (doubleComplementEq) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTnotintersectT) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementImpComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (contraSubsetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementTcontraSubset) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTILcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTIRcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (binunionTEcontra) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2a) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2b) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (demorgan2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule0) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz13rule4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_3) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_4) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz1_5) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1SetBreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (choice2fnsingleton) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1all1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (subbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (eqbreln1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1invE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1compEex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionprop) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIL) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionIR) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionI) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionE) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionEcases) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (breln1unionCommutes) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2W) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2A) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (woz2B) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Ex1) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1Equiv) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1E) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (image1I) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (injFuncSetFuncInj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (leftInvIsSurj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (surjCantorThm) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (foundation2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (notinself2) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSp) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (omegaSclos) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peano0notS) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (peanoSinj) =>
% 122.49/16.39                                                                     ((
% 122.49/16.39                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1195])).
% 122.49/16.40  thf(zip_derived_cl1207, plain,
% 122.49/16.40      (~ (((upairset2E) =>
% 122.49/16.40           (((upairsubunion) =>
% 122.49/16.40             (((upairinpowunion) =>
% 122.49/16.40               (((ubforcartprodlem1) =>
% 122.49/16.40                 (((ubforcartprodlem2) =>
% 122.49/16.40                   (((ubforcartprodlem3) =>
% 122.49/16.40                     (((cartprodpairin) =>
% 122.49/16.40                       (((cartprodmempair1) =>
% 122.49/16.40                         (((cartprodmempair) =>
% 122.49/16.40                           (((setunionE2) =>
% 122.49/16.40                             (((setunionsingleton1) =>
% 122.49/16.40                               (((setunionsingleton2) =>
% 122.49/16.40                                 (((setunionsingleton) =>
% 122.49/16.40                                   (((singletonprop) =>
% 122.49/16.40                                     (((ex1E1) =>
% 122.49/16.40                                       (((ex1I) =>
% 122.49/16.40                                         (((ex1I2) =>
% 122.49/16.40                                           (((singletonsuniq) =>
% 122.49/16.40                                             (((setukpairinjL1) =>
% 122.49/16.40                                               (((kfstsingleton) =>
% 122.49/16.40                                                 (((theprop) =>
% 122.49/16.40                                                   (((kfstpairEq) =>
% 122.49/16.40                                                     (((cartprodfstin) =>
% 122.49/16.40                                                       (((setukpairinjL2) =>
% 122.49/16.40                                                         (((setukpairinjL) =>
% 122.49/16.40                                                           (((setukpairinjR11) =>
% 122.49/16.40                                                             (((setukpairinjR12) =>
% 122.49/16.40                                                               (((setukpairinjR1) =>
% 122.49/16.40                                                                 (((upairequniteq) =>
% 122.49/16.40                                                                   (((setukpairinjR2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setukpairinjR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ksndsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ksndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (kpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndin) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemEL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodmempaircEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodfstpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1202])).
% 122.49/16.40  thf(zip_derived_cl1212, plain,
% 122.49/16.40      (~ (((upairsubunion) =>
% 122.49/16.40           (((upairinpowunion) =>
% 122.49/16.40             (((ubforcartprodlem1) =>
% 122.49/16.40               (((ubforcartprodlem2) =>
% 122.49/16.40                 (((ubforcartprodlem3) =>
% 122.49/16.40                   (((cartprodpairin) =>
% 122.49/16.40                     (((cartprodmempair1) =>
% 122.49/16.40                       (((cartprodmempair) =>
% 122.49/16.40                         (((setunionE2) =>
% 122.49/16.40                           (((setunionsingleton1) =>
% 122.49/16.40                             (((setunionsingleton2) =>
% 122.49/16.40                               (((setunionsingleton) =>
% 122.49/16.40                                 (((singletonprop) =>
% 122.49/16.40                                   (((ex1E1) =>
% 122.49/16.40                                     (((ex1I) =>
% 122.49/16.40                                       (((ex1I2) =>
% 122.49/16.40                                         (((singletonsuniq) =>
% 122.49/16.40                                           (((setukpairinjL1) =>
% 122.49/16.40                                             (((kfstsingleton) =>
% 122.49/16.40                                               (((theprop) =>
% 122.49/16.40                                                 (((kfstpairEq) =>
% 122.49/16.40                                                   (((cartprodfstin) =>
% 122.49/16.40                                                     (((setukpairinjL2) =>
% 122.49/16.40                                                       (((setukpairinjL) =>
% 122.49/16.40                                                         (((setukpairinjR11) =>
% 122.49/16.40                                                           (((setukpairinjR12) =>
% 122.49/16.40                                                             (((setukpairinjR1) =>
% 122.49/16.40                                                               (((upairequniteq) =>
% 122.49/16.40                                                                 (((setukpairinjR2) =>
% 122.49/16.40                                                                   (((setukpairinjR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ksndsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ksndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (kpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndin) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemEL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodmempaircEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodfstpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1207])).
% 122.49/16.40  thf(zip_derived_cl1218, plain,
% 122.49/16.40      (~ (((upairinpowunion) =>
% 122.49/16.40           (((ubforcartprodlem1) =>
% 122.49/16.40             (((ubforcartprodlem2) =>
% 122.49/16.40               (((ubforcartprodlem3) =>
% 122.49/16.40                 (((cartprodpairin) =>
% 122.49/16.40                   (((cartprodmempair1) =>
% 122.49/16.40                     (((cartprodmempair) =>
% 122.49/16.40                       (((setunionE2) =>
% 122.49/16.40                         (((setunionsingleton1) =>
% 122.49/16.40                           (((setunionsingleton2) =>
% 122.49/16.40                             (((setunionsingleton) =>
% 122.49/16.40                               (((singletonprop) =>
% 122.49/16.40                                 (((ex1E1) =>
% 122.49/16.40                                   (((ex1I) =>
% 122.49/16.40                                     (((ex1I2) =>
% 122.49/16.40                                       (((singletonsuniq) =>
% 122.49/16.40                                         (((setukpairinjL1) =>
% 122.49/16.40                                           (((kfstsingleton) =>
% 122.49/16.40                                             (((theprop) =>
% 122.49/16.40                                               (((kfstpairEq) =>
% 122.49/16.40                                                 (((cartprodfstin) =>
% 122.49/16.40                                                   (((setukpairinjL2) =>
% 122.49/16.40                                                     (((setukpairinjL) =>
% 122.49/16.40                                                       (((setukpairinjR11) =>
% 122.49/16.40                                                         (((setukpairinjR12) =>
% 122.49/16.40                                                           (((setukpairinjR1) =>
% 122.49/16.40                                                             (((upairequniteq) =>
% 122.49/16.40                                                               (((setukpairinjR2) =>
% 122.49/16.40                                                                 (((setukpairinjR) =>
% 122.49/16.40                                                                   (((ksndsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ksndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (kpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndin) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemEL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodmempaircEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodfstpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1212])).
% 122.49/16.40  thf(zip_derived_cl1224, plain,
% 122.49/16.40      (~ (((ubforcartprodlem1) =>
% 122.49/16.40           (((ubforcartprodlem2) =>
% 122.49/16.40             (((ubforcartprodlem3) =>
% 122.49/16.40               (((cartprodpairin) =>
% 122.49/16.40                 (((cartprodmempair1) =>
% 122.49/16.40                   (((cartprodmempair) =>
% 122.49/16.40                     (((setunionE2) =>
% 122.49/16.40                       (((setunionsingleton1) =>
% 122.49/16.40                         (((setunionsingleton2) =>
% 122.49/16.40                           (((setunionsingleton) =>
% 122.49/16.40                             (((singletonprop) =>
% 122.49/16.40                               (((ex1E1) =>
% 122.49/16.40                                 (((ex1I) =>
% 122.49/16.40                                   (((ex1I2) =>
% 122.49/16.40                                     (((singletonsuniq) =>
% 122.49/16.40                                       (((setukpairinjL1) =>
% 122.49/16.40                                         (((kfstsingleton) =>
% 122.49/16.40                                           (((theprop) =>
% 122.49/16.40                                             (((kfstpairEq) =>
% 122.49/16.40                                               (((cartprodfstin) =>
% 122.49/16.40                                                 (((setukpairinjL2) =>
% 122.49/16.40                                                   (((setukpairinjL) =>
% 122.49/16.40                                                     (((setukpairinjR11) =>
% 122.49/16.40                                                       (((setukpairinjR12) =>
% 122.49/16.40                                                         (((setukpairinjR1) =>
% 122.49/16.40                                                           (((upairequniteq) =>
% 122.49/16.40                                                             (((setukpairinjR2) =>
% 122.49/16.40                                                               (((setukpairinjR) =>
% 122.49/16.40                                                                 (((ksndsingleton) =>
% 122.49/16.40                                                                   (((ksndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (kpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndin) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemEL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodmempaircEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodfstpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1218])).
% 122.49/16.40  thf(zip_derived_cl1230, plain,
% 122.49/16.40      (~ (((ubforcartprodlem2) =>
% 122.49/16.40           (((ubforcartprodlem3) =>
% 122.49/16.40             (((cartprodpairin) =>
% 122.49/16.40               (((cartprodmempair1) =>
% 122.49/16.40                 (((cartprodmempair) =>
% 122.49/16.40                   (((setunionE2) =>
% 122.49/16.40                     (((setunionsingleton1) =>
% 122.49/16.40                       (((setunionsingleton2) =>
% 122.49/16.40                         (((setunionsingleton) =>
% 122.49/16.40                           (((singletonprop) =>
% 122.49/16.40                             (((ex1E1) =>
% 122.49/16.40                               (((ex1I) =>
% 122.49/16.40                                 (((ex1I2) =>
% 122.49/16.40                                   (((singletonsuniq) =>
% 122.49/16.40                                     (((setukpairinjL1) =>
% 122.49/16.40                                       (((kfstsingleton) =>
% 122.49/16.40                                         (((theprop) =>
% 122.49/16.40                                           (((kfstpairEq) =>
% 122.49/16.40                                             (((cartprodfstin) =>
% 122.49/16.40                                               (((setukpairinjL2) =>
% 122.49/16.40                                                 (((setukpairinjL) =>
% 122.49/16.40                                                   (((setukpairinjR11) =>
% 122.49/16.40                                                     (((setukpairinjR12) =>
% 122.49/16.40                                                       (((setukpairinjR1) =>
% 122.49/16.40                                                         (((upairequniteq) =>
% 122.49/16.40                                                           (((setukpairinjR2) =>
% 122.49/16.40                                                             (((setukpairinjR) =>
% 122.49/16.40                                                               (((ksndsingleton) =>
% 122.49/16.40                                                                 (((ksndpairEq) =>
% 122.49/16.40                                                                   (((kpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndin) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemEL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodmempaircEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodfstpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1224])).
% 122.49/16.40  thf(zip_derived_cl1237, plain,
% 122.49/16.40      (~ (((ubforcartprodlem3) =>
% 122.49/16.40           (((cartprodpairin) =>
% 122.49/16.40             (((cartprodmempair1) =>
% 122.49/16.40               (((cartprodmempair) =>
% 122.49/16.40                 (((setunionE2) =>
% 122.49/16.40                   (((setunionsingleton1) =>
% 122.49/16.40                     (((setunionsingleton2) =>
% 122.49/16.40                       (((setunionsingleton) =>
% 122.49/16.40                         (((singletonprop) =>
% 122.49/16.40                           (((ex1E1) =>
% 122.49/16.40                             (((ex1I) =>
% 122.49/16.40                               (((ex1I2) =>
% 122.49/16.40                                 (((singletonsuniq) =>
% 122.49/16.40                                   (((setukpairinjL1) =>
% 122.49/16.40                                     (((kfstsingleton) =>
% 122.49/16.40                                       (((theprop) =>
% 122.49/16.40                                         (((kfstpairEq) =>
% 122.49/16.40                                           (((cartprodfstin) =>
% 122.49/16.40                                             (((setukpairinjL2) =>
% 122.49/16.40                                               (((setukpairinjL) =>
% 122.49/16.40                                                 (((setukpairinjR11) =>
% 122.49/16.40                                                   (((setukpairinjR12) =>
% 122.49/16.40                                                     (((setukpairinjR1) =>
% 122.49/16.40                                                       (((upairequniteq) =>
% 122.49/16.40                                                         (((setukpairinjR2) =>
% 122.49/16.40                                                           (((setukpairinjR) =>
% 122.49/16.40                                                             (((ksndsingleton) =>
% 122.49/16.40                                                               (((ksndpairEq) =>
% 122.49/16.40                                                                 (((kpairsurjEq) =>
% 122.49/16.40                                                                   (((cartprodsndin) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemEL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodmempaircEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodfstpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1230])).
% 122.49/16.40  thf(zip_derived_cl1244, plain,
% 122.49/16.40      (~ (((cartprodpairin) =>
% 122.49/16.40           (((cartprodmempair1) =>
% 122.49/16.40             (((cartprodmempair) =>
% 122.49/16.40               (((setunionE2) =>
% 122.49/16.40                 (((setunionsingleton1) =>
% 122.49/16.40                   (((setunionsingleton2) =>
% 122.49/16.40                     (((setunionsingleton) =>
% 122.49/16.40                       (((singletonprop) =>
% 122.49/16.40                         (((ex1E1) =>
% 122.49/16.40                           (((ex1I) =>
% 122.49/16.40                             (((ex1I2) =>
% 122.49/16.40                               (((singletonsuniq) =>
% 122.49/16.40                                 (((setukpairinjL1) =>
% 122.49/16.40                                   (((kfstsingleton) =>
% 122.49/16.40                                     (((theprop) =>
% 122.49/16.40                                       (((kfstpairEq) =>
% 122.49/16.40                                         (((cartprodfstin) =>
% 122.49/16.40                                           (((setukpairinjL2) =>
% 122.49/16.40                                             (((setukpairinjL) =>
% 122.49/16.40                                               (((setukpairinjR11) =>
% 122.49/16.40                                                 (((setukpairinjR12) =>
% 122.49/16.40                                                   (((setukpairinjR1) =>
% 122.49/16.40                                                     (((upairequniteq) =>
% 122.49/16.40                                                       (((setukpairinjR2) =>
% 122.49/16.40                                                         (((setukpairinjR) =>
% 122.49/16.40                                                           (((ksndsingleton) =>
% 122.49/16.40                                                             (((ksndpairEq) =>
% 122.49/16.40                                                               (((kpairsurjEq) =>
% 122.49/16.40                                                                 (((cartprodsndin) =>
% 122.49/16.40                                                                   (((cartprodpairmemEL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairmemER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodmempaircEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodfstpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1237])).
% 122.49/16.40  thf(zip_derived_cl1252, plain,
% 122.49/16.40      (~ (((cartprodmempair1) =>
% 122.49/16.40           (((cartprodmempair) =>
% 122.49/16.40             (((setunionE2) =>
% 122.49/16.40               (((setunionsingleton1) =>
% 122.49/16.40                 (((setunionsingleton2) =>
% 122.49/16.40                   (((setunionsingleton) =>
% 122.49/16.40                     (((singletonprop) =>
% 122.49/16.40                       (((ex1E1) =>
% 122.49/16.40                         (((ex1I) =>
% 122.49/16.40                           (((ex1I2) =>
% 122.49/16.40                             (((singletonsuniq) =>
% 122.49/16.40                               (((setukpairinjL1) =>
% 122.49/16.40                                 (((kfstsingleton) =>
% 122.49/16.40                                   (((theprop) =>
% 122.49/16.40                                     (((kfstpairEq) =>
% 122.49/16.40                                       (((cartprodfstin) =>
% 122.49/16.40                                         (((setukpairinjL2) =>
% 122.49/16.40                                           (((setukpairinjL) =>
% 122.49/16.40                                             (((setukpairinjR11) =>
% 122.49/16.40                                               (((setukpairinjR12) =>
% 122.49/16.40                                                 (((setukpairinjR1) =>
% 122.49/16.40                                                   (((upairequniteq) =>
% 122.49/16.40                                                     (((setukpairinjR2) =>
% 122.49/16.40                                                       (((setukpairinjR) =>
% 122.49/16.40                                                         (((ksndsingleton) =>
% 122.49/16.40                                                           (((ksndpairEq) =>
% 122.49/16.40                                                             (((kpairsurjEq) =>
% 122.49/16.40                                                               (((cartprodsndin) =>
% 122.49/16.40                                                                 (((cartprodpairmemEL) =>
% 122.49/16.40                                                                   (((cartprodpairmemER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodmempaircEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodfstpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1244])).
% 122.49/16.40  thf(zip_derived_cl1261, plain,
% 122.49/16.40      (~ (((cartprodmempair) =>
% 122.49/16.40           (((setunionE2) =>
% 122.49/16.40             (((setunionsingleton1) =>
% 122.49/16.40               (((setunionsingleton2) =>
% 122.49/16.40                 (((setunionsingleton) =>
% 122.49/16.40                   (((singletonprop) =>
% 122.49/16.40                     (((ex1E1) =>
% 122.49/16.40                       (((ex1I) =>
% 122.49/16.40                         (((ex1I2) =>
% 122.49/16.40                           (((singletonsuniq) =>
% 122.49/16.40                             (((setukpairinjL1) =>
% 122.49/16.40                               (((kfstsingleton) =>
% 122.49/16.40                                 (((theprop) =>
% 122.49/16.40                                   (((kfstpairEq) =>
% 122.49/16.40                                     (((cartprodfstin) =>
% 122.49/16.40                                       (((setukpairinjL2) =>
% 122.49/16.40                                         (((setukpairinjL) =>
% 122.49/16.40                                           (((setukpairinjR11) =>
% 122.49/16.40                                             (((setukpairinjR12) =>
% 122.49/16.40                                               (((setukpairinjR1) =>
% 122.49/16.40                                                 (((upairequniteq) =>
% 122.49/16.40                                                   (((setukpairinjR2) =>
% 122.49/16.40                                                     (((setukpairinjR) =>
% 122.49/16.40                                                       (((ksndsingleton) =>
% 122.49/16.40                                                         (((ksndpairEq) =>
% 122.49/16.40                                                           (((kpairsurjEq) =>
% 122.49/16.40                                                             (((cartprodsndin) =>
% 122.49/16.40                                                               (((cartprodpairmemEL) =>
% 122.49/16.40                                                                 (((cartprodpairmemER) =>
% 122.49/16.40                                                                   (((cartprodmempaircEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodfstpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1252])).
% 122.49/16.40  thf(zip_derived_cl1270, plain,
% 122.49/16.40      (~ (((setunionE2) =>
% 122.49/16.40           (((setunionsingleton1) =>
% 122.49/16.40             (((setunionsingleton2) =>
% 122.49/16.40               (((setunionsingleton) =>
% 122.49/16.40                 (((singletonprop) =>
% 122.49/16.40                   (((ex1E1) =>
% 122.49/16.40                     (((ex1I) =>
% 122.49/16.40                       (((ex1I2) =>
% 122.49/16.40                         (((singletonsuniq) =>
% 122.49/16.40                           (((setukpairinjL1) =>
% 122.49/16.40                             (((kfstsingleton) =>
% 122.49/16.40                               (((theprop) =>
% 122.49/16.40                                 (((kfstpairEq) =>
% 122.49/16.40                                   (((cartprodfstin) =>
% 122.49/16.40                                     (((setukpairinjL2) =>
% 122.49/16.40                                       (((setukpairinjL) =>
% 122.49/16.40                                         (((setukpairinjR11) =>
% 122.49/16.40                                           (((setukpairinjR12) =>
% 122.49/16.40                                             (((setukpairinjR1) =>
% 122.49/16.40                                               (((upairequniteq) =>
% 122.49/16.40                                                 (((setukpairinjR2) =>
% 122.49/16.40                                                   (((setukpairinjR) =>
% 122.49/16.40                                                     (((ksndsingleton) =>
% 122.49/16.40                                                       (((ksndpairEq) =>
% 122.49/16.40                                                         (((kpairsurjEq) =>
% 122.49/16.40                                                           (((cartprodsndin) =>
% 122.49/16.40                                                             (((cartprodpairmemEL) =>
% 122.49/16.40                                                               (((cartprodpairmemER) =>
% 122.49/16.40                                                                 (((cartprodmempaircEq) =>
% 122.49/16.40                                                                   (((cartprodfstpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodsndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1261])).
% 122.49/16.40  thf(zip_derived_cl1279, plain,
% 122.49/16.40      (~ (((setunionsingleton1) =>
% 122.49/16.40           (((setunionsingleton2) =>
% 122.49/16.40             (((setunionsingleton) =>
% 122.49/16.40               (((singletonprop) =>
% 122.49/16.40                 (((ex1E1) =>
% 122.49/16.40                   (((ex1I) =>
% 122.49/16.40                     (((ex1I2) =>
% 122.49/16.40                       (((singletonsuniq) =>
% 122.49/16.40                         (((setukpairinjL1) =>
% 122.49/16.40                           (((kfstsingleton) =>
% 122.49/16.40                             (((theprop) =>
% 122.49/16.40                               (((kfstpairEq) =>
% 122.49/16.40                                 (((cartprodfstin) =>
% 122.49/16.40                                   (((setukpairinjL2) =>
% 122.49/16.40                                     (((setukpairinjL) =>
% 122.49/16.40                                       (((setukpairinjR11) =>
% 122.49/16.40                                         (((setukpairinjR12) =>
% 122.49/16.40                                           (((setukpairinjR1) =>
% 122.49/16.40                                             (((upairequniteq) =>
% 122.49/16.40                                               (((setukpairinjR2) =>
% 122.49/16.40                                                 (((setukpairinjR) =>
% 122.49/16.40                                                   (((ksndsingleton) =>
% 122.49/16.40                                                     (((ksndpairEq) =>
% 122.49/16.40                                                       (((kpairsurjEq) =>
% 122.49/16.40                                                         (((cartprodsndin) =>
% 122.49/16.40                                                           (((cartprodpairmemEL) =>
% 122.49/16.40                                                             (((cartprodpairmemER) =>
% 122.49/16.40                                                               (((cartprodmempaircEq) =>
% 122.49/16.40                                                                 (((cartprodfstpairEq) =>
% 122.49/16.40                                                                   (((cartprodsndpairEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (cartprodpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1270])).
% 122.49/16.40  thf(zip_derived_cl1288, plain,
% 122.49/16.40      (~ (((setunionsingleton2) =>
% 122.49/16.40           (((setunionsingleton) =>
% 122.49/16.40             (((singletonprop) =>
% 122.49/16.40               (((ex1E1) =>
% 122.49/16.40                 (((ex1I) =>
% 122.49/16.40                   (((ex1I2) =>
% 122.49/16.40                     (((singletonsuniq) =>
% 122.49/16.40                       (((setukpairinjL1) =>
% 122.49/16.40                         (((kfstsingleton) =>
% 122.49/16.40                           (((theprop) =>
% 122.49/16.40                             (((kfstpairEq) =>
% 122.49/16.40                               (((cartprodfstin) =>
% 122.49/16.40                                 (((setukpairinjL2) =>
% 122.49/16.40                                   (((setukpairinjL) =>
% 122.49/16.40                                     (((setukpairinjR11) =>
% 122.49/16.40                                       (((setukpairinjR12) =>
% 122.49/16.40                                         (((setukpairinjR1) =>
% 122.49/16.40                                           (((upairequniteq) =>
% 122.49/16.40                                             (((setukpairinjR2) =>
% 122.49/16.40                                               (((setukpairinjR) =>
% 122.49/16.40                                                 (((ksndsingleton) =>
% 122.49/16.40                                                   (((ksndpairEq) =>
% 122.49/16.40                                                     (((kpairsurjEq) =>
% 122.49/16.40                                                       (((cartprodsndin) =>
% 122.49/16.40                                                         (((cartprodpairmemEL) =>
% 122.49/16.40                                                           (((cartprodpairmemER) =>
% 122.49/16.40                                                             (((cartprodmempaircEq) =>
% 122.49/16.40                                                               (((cartprodfstpairEq) =>
% 122.49/16.40                                                                 (((cartprodsndpairEq) =>
% 122.49/16.40                                                                   (((cartprodpairsurjEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1279])).
% 122.49/16.40  thf(zip_derived_cl1297, plain,
% 122.49/16.40      (~ (((setunionsingleton) =>
% 122.49/16.40           (((singletonprop) =>
% 122.49/16.40             (((ex1E1) =>
% 122.49/16.40               (((ex1I) =>
% 122.49/16.40                 (((ex1I2) =>
% 122.49/16.40                   (((singletonsuniq) =>
% 122.49/16.40                     (((setukpairinjL1) =>
% 122.49/16.40                       (((kfstsingleton) =>
% 122.49/16.40                         (((theprop) =>
% 122.49/16.40                           (((kfstpairEq) =>
% 122.49/16.40                             (((cartprodfstin) =>
% 122.49/16.40                               (((setukpairinjL2) =>
% 122.49/16.40                                 (((setukpairinjL) =>
% 122.49/16.40                                   (((setukpairinjR11) =>
% 122.49/16.40                                     (((setukpairinjR12) =>
% 122.49/16.40                                       (((setukpairinjR1) =>
% 122.49/16.40                                         (((upairequniteq) =>
% 122.49/16.40                                           (((setukpairinjR2) =>
% 122.49/16.40                                             (((setukpairinjR) =>
% 122.49/16.40                                               (((ksndsingleton) =>
% 122.49/16.40                                                 (((ksndpairEq) =>
% 122.49/16.40                                                   (((kpairsurjEq) =>
% 122.49/16.40                                                     (((cartprodsndin) =>
% 122.49/16.40                                                       (((cartprodpairmemEL) =>
% 122.49/16.40                                                         (((cartprodpairmemER) =>
% 122.49/16.40                                                           (((cartprodmempaircEq) =>
% 122.49/16.40                                                             (((cartprodfstpairEq) =>
% 122.49/16.40                                                               (((cartprodsndpairEq) =>
% 122.49/16.40                                                                 (((cartprodpairsurjEq) =>
% 122.49/16.40                                                                   (((dpsetconstrI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1288])).
% 122.49/16.40  thf(zip_derived_cl1306, plain,
% 122.49/16.40      (~ (((singletonprop) =>
% 122.49/16.40           (((ex1E1) =>
% 122.49/16.40             (((ex1I) =>
% 122.49/16.40               (((ex1I2) =>
% 122.49/16.40                 (((singletonsuniq) =>
% 122.49/16.40                   (((setukpairinjL1) =>
% 122.49/16.40                     (((kfstsingleton) =>
% 122.49/16.40                       (((theprop) =>
% 122.49/16.40                         (((kfstpairEq) =>
% 122.49/16.40                           (((cartprodfstin) =>
% 122.49/16.40                             (((setukpairinjL2) =>
% 122.49/16.40                               (((setukpairinjL) =>
% 122.49/16.40                                 (((setukpairinjR11) =>
% 122.49/16.40                                   (((setukpairinjR12) =>
% 122.49/16.40                                     (((setukpairinjR1) =>
% 122.49/16.40                                       (((upairequniteq) =>
% 122.49/16.40                                         (((setukpairinjR2) =>
% 122.49/16.40                                           (((setukpairinjR) =>
% 122.49/16.40                                             (((ksndsingleton) =>
% 122.49/16.40                                               (((ksndpairEq) =>
% 122.49/16.40                                                 (((kpairsurjEq) =>
% 122.49/16.40                                                   (((cartprodsndin) =>
% 122.49/16.40                                                     (((cartprodpairmemEL) =>
% 122.49/16.40                                                       (((cartprodpairmemER) =>
% 122.49/16.40                                                         (((cartprodmempaircEq) =>
% 122.49/16.40                                                           (((cartprodfstpairEq) =>
% 122.49/16.40                                                             (((cartprodsndpairEq) =>
% 122.49/16.40                                                               (((cartprodpairsurjEq) =>
% 122.49/16.40                                                                 (((dpsetconstrI) =>
% 122.49/16.40                                                                   (((dpsetconstrSub) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ifp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (theeq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrue) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueorfalse) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setminusT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementT_lem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setextT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subsetTI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (powersetTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTELcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintersectTERcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contrasubsetT3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementI1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementE1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementSub2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (doubleComplementEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTnotintersectT) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementImpComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (contraSubsetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementTcontraSubset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTILcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTIRcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binunionTEcontra) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2a) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2b) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (demorgan2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule0) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz13rule4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz1_5) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1SetBreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (choice2fnsingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1all1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1invE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1compEex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionprop) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIL) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionIR) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionI) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionE) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionEcases) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (breln1unionCommutes) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2W) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2A) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (woz2B) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Ex1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1Equiv) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1E) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (image1I) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (injFuncSetFuncInj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (leftInvIsSurj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (surjCantorThm) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (foundation2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (notinself2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (omegaSclos) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peano0notS) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (peanoSinj) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (binintTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (transitivesetOp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (setunionTransitive) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ordinalMinLem1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (!!) @ (
% 122.49/16.40                                                                     ^[Y0 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (ordinal @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y1 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (!!) @ (
% 122.49/16.40                                                                      ^[Y2 : $i]:
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y2 @ 
% 122.49/16.40                                                                      Y0) =>
% 122.49/16.40                                                                      ((
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ 
% 122.49/16.40                                                                      Y2) =>
% 122.49/16.40                                                                      (in @ 
% 122.49/16.40                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.40      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1297])).
% 122.49/16.40  thf(zip_derived_cl1314, plain,
% 122.49/16.40      (~ (((ex1E1) =>
% 122.49/16.40           (((ex1I) =>
% 122.49/16.40             (((ex1I2) =>
% 122.49/16.40               (((singletonsuniq) =>
% 122.49/16.40                 (((setukpairinjL1) =>
% 122.49/16.40                   (((kfstsingleton) =>
% 122.49/16.40                     (((theprop) =>
% 122.49/16.40                       (((kfstpairEq) =>
% 122.49/16.40                         (((cartprodfstin) =>
% 122.49/16.40                           (((setukpairinjL2) =>
% 122.49/16.40                             (((setukpairinjL) =>
% 122.49/16.40                               (((setukpairinjR11) =>
% 122.49/16.40                                 (((setukpairinjR12) =>
% 122.49/16.40                                   (((setukpairinjR1) =>
% 122.49/16.40                                     (((upairequniteq) =>
% 122.49/16.40                                       (((setukpairinjR2) =>
% 122.49/16.40                                         (((setukpairinjR) =>
% 122.49/16.40                                           (((ksndsingleton) =>
% 122.49/16.40                                             (((ksndpairEq) =>
% 122.49/16.40                                               (((kpairsurjEq) =>
% 122.49/16.40                                                 (((cartprodsndin) =>
% 122.49/16.40                                                   (((cartprodpairmemEL) =>
% 122.49/16.40                                                     (((cartprodpairmemER) =>
% 122.49/16.40                                                       (((cartprodmempaircEq) =>
% 122.49/16.40                                                         (((cartprodfstpairEq) =>
% 122.49/16.40                                                           (((cartprodsndpairEq) =>
% 122.49/16.40                                                             (((cartprodpairsurjEq) =>
% 122.49/16.40                                                               (((dpsetconstrI) =>
% 122.49/16.40                                                                 (((dpsetconstrSub) =>
% 122.49/16.40                                                                   (((setOfPairsIsBReln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrERa) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrEL2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (dpsetconstrER) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcImageSingleton) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (apProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (app) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (infuncsetfunc) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcinfuncset) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamProp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lamp) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2p) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (brelnall2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ex1E2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp3) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcextLem) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcGraphProp4) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (subbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eqbreln) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (funcext2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (ap2apEq2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (lam2lamEq) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (beta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (eta2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iffalseProp2) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp1) =>
% 122.49/16.40                                                                     ((
% 122.49/16.40                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1306])).
% 122.49/16.41  thf(zip_derived_cl1321, plain,
% 122.49/16.41      (~ (((ex1I) =>
% 122.49/16.41           (((ex1I2) =>
% 122.49/16.41             (((singletonsuniq) =>
% 122.49/16.41               (((setukpairinjL1) =>
% 122.49/16.41                 (((kfstsingleton) =>
% 122.49/16.41                   (((theprop) =>
% 122.49/16.41                     (((kfstpairEq) =>
% 122.49/16.41                       (((cartprodfstin) =>
% 122.49/16.41                         (((setukpairinjL2) =>
% 122.49/16.41                           (((setukpairinjL) =>
% 122.49/16.41                             (((setukpairinjR11) =>
% 122.49/16.41                               (((setukpairinjR12) =>
% 122.49/16.41                                 (((setukpairinjR1) =>
% 122.49/16.41                                   (((upairequniteq) =>
% 122.49/16.41                                     (((setukpairinjR2) =>
% 122.49/16.41                                       (((setukpairinjR) =>
% 122.49/16.41                                         (((ksndsingleton) =>
% 122.49/16.41                                           (((ksndpairEq) =>
% 122.49/16.41                                             (((kpairsurjEq) =>
% 122.49/16.41                                               (((cartprodsndin) =>
% 122.49/16.41                                                 (((cartprodpairmemEL) =>
% 122.49/16.41                                                   (((cartprodpairmemER) =>
% 122.49/16.41                                                     (((cartprodmempaircEq) =>
% 122.49/16.41                                                       (((cartprodfstpairEq) =>
% 122.49/16.41                                                         (((cartprodsndpairEq) =>
% 122.49/16.41                                                           (((cartprodpairsurjEq) =>
% 122.49/16.41                                                             (((dpsetconstrI) =>
% 122.49/16.41                                                               (((dpsetconstrSub) =>
% 122.49/16.41                                                                 (((setOfPairsIsBReln) =>
% 122.49/16.41                                                                   (((dpsetconstrERa) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (dpsetconstrEL1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (dpsetconstrEL2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (dpsetconstrER) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcImageSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (apProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (app) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (infuncsetfunc) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcinfuncset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1314])).
% 122.49/16.41  thf(zip_derived_cl1328, plain,
% 122.49/16.41      (~ (((ex1I2) =>
% 122.49/16.41           (((singletonsuniq) =>
% 122.49/16.41             (((setukpairinjL1) =>
% 122.49/16.41               (((kfstsingleton) =>
% 122.49/16.41                 (((theprop) =>
% 122.49/16.41                   (((kfstpairEq) =>
% 122.49/16.41                     (((cartprodfstin) =>
% 122.49/16.41                       (((setukpairinjL2) =>
% 122.49/16.41                         (((setukpairinjL) =>
% 122.49/16.41                           (((setukpairinjR11) =>
% 122.49/16.41                             (((setukpairinjR12) =>
% 122.49/16.41                               (((setukpairinjR1) =>
% 122.49/16.41                                 (((upairequniteq) =>
% 122.49/16.41                                   (((setukpairinjR2) =>
% 122.49/16.41                                     (((setukpairinjR) =>
% 122.49/16.41                                       (((ksndsingleton) =>
% 122.49/16.41                                         (((ksndpairEq) =>
% 122.49/16.41                                           (((kpairsurjEq) =>
% 122.49/16.41                                             (((cartprodsndin) =>
% 122.49/16.41                                               (((cartprodpairmemEL) =>
% 122.49/16.41                                                 (((cartprodpairmemER) =>
% 122.49/16.41                                                   (((cartprodmempaircEq) =>
% 122.49/16.41                                                     (((cartprodfstpairEq) =>
% 122.49/16.41                                                       (((cartprodsndpairEq) =>
% 122.49/16.41                                                         (((cartprodpairsurjEq) =>
% 122.49/16.41                                                           (((dpsetconstrI) =>
% 122.49/16.41                                                             (((dpsetconstrSub) =>
% 122.49/16.41                                                               (((setOfPairsIsBReln) =>
% 122.49/16.41                                                                 (((dpsetconstrERa) =>
% 122.49/16.41                                                                   (((dpsetconstrEL1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (dpsetconstrEL2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (dpsetconstrER) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcImageSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (apProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (app) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (infuncsetfunc) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcinfuncset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1321])).
% 122.49/16.41  thf(zip_derived_cl1336, plain,
% 122.49/16.41      (~ (((singletonsuniq) =>
% 122.49/16.41           (((setukpairinjL1) =>
% 122.49/16.41             (((kfstsingleton) =>
% 122.49/16.41               (((theprop) =>
% 122.49/16.41                 (((kfstpairEq) =>
% 122.49/16.41                   (((cartprodfstin) =>
% 122.49/16.41                     (((setukpairinjL2) =>
% 122.49/16.41                       (((setukpairinjL) =>
% 122.49/16.41                         (((setukpairinjR11) =>
% 122.49/16.41                           (((setukpairinjR12) =>
% 122.49/16.41                             (((setukpairinjR1) =>
% 122.49/16.41                               (((upairequniteq) =>
% 122.49/16.41                                 (((setukpairinjR2) =>
% 122.49/16.41                                   (((setukpairinjR) =>
% 122.49/16.41                                     (((ksndsingleton) =>
% 122.49/16.41                                       (((ksndpairEq) =>
% 122.49/16.41                                         (((kpairsurjEq) =>
% 122.49/16.41                                           (((cartprodsndin) =>
% 122.49/16.41                                             (((cartprodpairmemEL) =>
% 122.49/16.41                                               (((cartprodpairmemER) =>
% 122.49/16.41                                                 (((cartprodmempaircEq) =>
% 122.49/16.41                                                   (((cartprodfstpairEq) =>
% 122.49/16.41                                                     (((cartprodsndpairEq) =>
% 122.49/16.41                                                       (((cartprodpairsurjEq) =>
% 122.49/16.41                                                         (((dpsetconstrI) =>
% 122.49/16.41                                                           (((dpsetconstrSub) =>
% 122.49/16.41                                                             (((setOfPairsIsBReln) =>
% 122.49/16.41                                                               (((dpsetconstrERa) =>
% 122.49/16.41                                                                 (((dpsetconstrEL1) =>
% 122.49/16.41                                                                   (((dpsetconstrEL2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (dpsetconstrER) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcImageSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (apProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (app) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (infuncsetfunc) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcinfuncset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1328])).
% 122.49/16.41  thf(zip_derived_cl1344, plain,
% 122.49/16.41      (~ (((setukpairinjL1) =>
% 122.49/16.41           (((kfstsingleton) =>
% 122.49/16.41             (((theprop) =>
% 122.49/16.41               (((kfstpairEq) =>
% 122.49/16.41                 (((cartprodfstin) =>
% 122.49/16.41                   (((setukpairinjL2) =>
% 122.49/16.41                     (((setukpairinjL) =>
% 122.49/16.41                       (((setukpairinjR11) =>
% 122.49/16.41                         (((setukpairinjR12) =>
% 122.49/16.41                           (((setukpairinjR1) =>
% 122.49/16.41                             (((upairequniteq) =>
% 122.49/16.41                               (((setukpairinjR2) =>
% 122.49/16.41                                 (((setukpairinjR) =>
% 122.49/16.41                                   (((ksndsingleton) =>
% 122.49/16.41                                     (((ksndpairEq) =>
% 122.49/16.41                                       (((kpairsurjEq) =>
% 122.49/16.41                                         (((cartprodsndin) =>
% 122.49/16.41                                           (((cartprodpairmemEL) =>
% 122.49/16.41                                             (((cartprodpairmemER) =>
% 122.49/16.41                                               (((cartprodmempaircEq) =>
% 122.49/16.41                                                 (((cartprodfstpairEq) =>
% 122.49/16.41                                                   (((cartprodsndpairEq) =>
% 122.49/16.41                                                     (((cartprodpairsurjEq) =>
% 122.49/16.41                                                       (((dpsetconstrI) =>
% 122.49/16.41                                                         (((dpsetconstrSub) =>
% 122.49/16.41                                                           (((setOfPairsIsBReln) =>
% 122.49/16.41                                                             (((dpsetconstrERa) =>
% 122.49/16.41                                                               (((dpsetconstrEL1) =>
% 122.49/16.41                                                                 (((dpsetconstrEL2) =>
% 122.49/16.41                                                                   (((dpsetconstrER) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcImageSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (apProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (app) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (infuncsetfunc) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcinfuncset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1336])).
% 122.49/16.41  thf(zip_derived_cl1352, plain,
% 122.49/16.41      (~ (((kfstsingleton) =>
% 122.49/16.41           (((theprop) =>
% 122.49/16.41             (((kfstpairEq) =>
% 122.49/16.41               (((cartprodfstin) =>
% 122.49/16.41                 (((setukpairinjL2) =>
% 122.49/16.41                   (((setukpairinjL) =>
% 122.49/16.41                     (((setukpairinjR11) =>
% 122.49/16.41                       (((setukpairinjR12) =>
% 122.49/16.41                         (((setukpairinjR1) =>
% 122.49/16.41                           (((upairequniteq) =>
% 122.49/16.41                             (((setukpairinjR2) =>
% 122.49/16.41                               (((setukpairinjR) =>
% 122.49/16.41                                 (((ksndsingleton) =>
% 122.49/16.41                                   (((ksndpairEq) =>
% 122.49/16.41                                     (((kpairsurjEq) =>
% 122.49/16.41                                       (((cartprodsndin) =>
% 122.49/16.41                                         (((cartprodpairmemEL) =>
% 122.49/16.41                                           (((cartprodpairmemER) =>
% 122.49/16.41                                             (((cartprodmempaircEq) =>
% 122.49/16.41                                               (((cartprodfstpairEq) =>
% 122.49/16.41                                                 (((cartprodsndpairEq) =>
% 122.49/16.41                                                   (((cartprodpairsurjEq) =>
% 122.49/16.41                                                     (((dpsetconstrI) =>
% 122.49/16.41                                                       (((dpsetconstrSub) =>
% 122.49/16.41                                                         (((setOfPairsIsBReln) =>
% 122.49/16.41                                                           (((dpsetconstrERa) =>
% 122.49/16.41                                                             (((dpsetconstrEL1) =>
% 122.49/16.41                                                               (((dpsetconstrEL2) =>
% 122.49/16.41                                                                 (((dpsetconstrER) =>
% 122.49/16.41                                                                   (((funcImageSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (apProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (app) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (infuncsetfunc) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcinfuncset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1344])).
% 122.49/16.41  thf(zip_derived_cl1361, plain,
% 122.49/16.41      (~ (((theprop) =>
% 122.49/16.41           (((kfstpairEq) =>
% 122.49/16.41             (((cartprodfstin) =>
% 122.49/16.41               (((setukpairinjL2) =>
% 122.49/16.41                 (((setukpairinjL) =>
% 122.49/16.41                   (((setukpairinjR11) =>
% 122.49/16.41                     (((setukpairinjR12) =>
% 122.49/16.41                       (((setukpairinjR1) =>
% 122.49/16.41                         (((upairequniteq) =>
% 122.49/16.41                           (((setukpairinjR2) =>
% 122.49/16.41                             (((setukpairinjR) =>
% 122.49/16.41                               (((ksndsingleton) =>
% 122.49/16.41                                 (((ksndpairEq) =>
% 122.49/16.41                                   (((kpairsurjEq) =>
% 122.49/16.41                                     (((cartprodsndin) =>
% 122.49/16.41                                       (((cartprodpairmemEL) =>
% 122.49/16.41                                         (((cartprodpairmemER) =>
% 122.49/16.41                                           (((cartprodmempaircEq) =>
% 122.49/16.41                                             (((cartprodfstpairEq) =>
% 122.49/16.41                                               (((cartprodsndpairEq) =>
% 122.49/16.41                                                 (((cartprodpairsurjEq) =>
% 122.49/16.41                                                   (((dpsetconstrI) =>
% 122.49/16.41                                                     (((dpsetconstrSub) =>
% 122.49/16.41                                                       (((setOfPairsIsBReln) =>
% 122.49/16.41                                                         (((dpsetconstrERa) =>
% 122.49/16.41                                                           (((dpsetconstrEL1) =>
% 122.49/16.41                                                             (((dpsetconstrEL2) =>
% 122.49/16.41                                                               (((dpsetconstrER) =>
% 122.49/16.41                                                                 (((funcImageSingleton) =>
% 122.49/16.41                                                                   (((apProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (app) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (infuncsetfunc) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcinfuncset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1352])).
% 122.49/16.41  thf(zip_derived_cl1371, plain,
% 122.49/16.41      (~ (((kfstpairEq) =>
% 122.49/16.41           (((cartprodfstin) =>
% 122.49/16.41             (((setukpairinjL2) =>
% 122.49/16.41               (((setukpairinjL) =>
% 122.49/16.41                 (((setukpairinjR11) =>
% 122.49/16.41                   (((setukpairinjR12) =>
% 122.49/16.41                     (((setukpairinjR1) =>
% 122.49/16.41                       (((upairequniteq) =>
% 122.49/16.41                         (((setukpairinjR2) =>
% 122.49/16.41                           (((setukpairinjR) =>
% 122.49/16.41                             (((ksndsingleton) =>
% 122.49/16.41                               (((ksndpairEq) =>
% 122.49/16.41                                 (((kpairsurjEq) =>
% 122.49/16.41                                   (((cartprodsndin) =>
% 122.49/16.41                                     (((cartprodpairmemEL) =>
% 122.49/16.41                                       (((cartprodpairmemER) =>
% 122.49/16.41                                         (((cartprodmempaircEq) =>
% 122.49/16.41                                           (((cartprodfstpairEq) =>
% 122.49/16.41                                             (((cartprodsndpairEq) =>
% 122.49/16.41                                               (((cartprodpairsurjEq) =>
% 122.49/16.41                                                 (((dpsetconstrI) =>
% 122.49/16.41                                                   (((dpsetconstrSub) =>
% 122.49/16.41                                                     (((setOfPairsIsBReln) =>
% 122.49/16.41                                                       (((dpsetconstrERa) =>
% 122.49/16.41                                                         (((dpsetconstrEL1) =>
% 122.49/16.41                                                           (((dpsetconstrEL2) =>
% 122.49/16.41                                                             (((dpsetconstrER) =>
% 122.49/16.41                                                               (((funcImageSingleton) =>
% 122.49/16.41                                                                 (((apProp) =>
% 122.49/16.41                                                                   (((app) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (infuncsetfunc) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcinfuncset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1361])).
% 122.49/16.41  thf(zip_derived_cl1382, plain,
% 122.49/16.41      (~ (((cartprodfstin) =>
% 122.49/16.41           (((setukpairinjL2) =>
% 122.49/16.41             (((setukpairinjL) =>
% 122.49/16.41               (((setukpairinjR11) =>
% 122.49/16.41                 (((setukpairinjR12) =>
% 122.49/16.41                   (((setukpairinjR1) =>
% 122.49/16.41                     (((upairequniteq) =>
% 122.49/16.41                       (((setukpairinjR2) =>
% 122.49/16.41                         (((setukpairinjR) =>
% 122.49/16.41                           (((ksndsingleton) =>
% 122.49/16.41                             (((ksndpairEq) =>
% 122.49/16.41                               (((kpairsurjEq) =>
% 122.49/16.41                                 (((cartprodsndin) =>
% 122.49/16.41                                   (((cartprodpairmemEL) =>
% 122.49/16.41                                     (((cartprodpairmemER) =>
% 122.49/16.41                                       (((cartprodmempaircEq) =>
% 122.49/16.41                                         (((cartprodfstpairEq) =>
% 122.49/16.41                                           (((cartprodsndpairEq) =>
% 122.49/16.41                                             (((cartprodpairsurjEq) =>
% 122.49/16.41                                               (((dpsetconstrI) =>
% 122.49/16.41                                                 (((dpsetconstrSub) =>
% 122.49/16.41                                                   (((setOfPairsIsBReln) =>
% 122.49/16.41                                                     (((dpsetconstrERa) =>
% 122.49/16.41                                                       (((dpsetconstrEL1) =>
% 122.49/16.41                                                         (((dpsetconstrEL2) =>
% 122.49/16.41                                                           (((dpsetconstrER) =>
% 122.49/16.41                                                             (((funcImageSingleton) =>
% 122.49/16.41                                                               (((apProp) =>
% 122.49/16.41                                                                 (((app) =>
% 122.49/16.41                                                                   (((infuncsetfunc) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcinfuncset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1371])).
% 122.49/16.41  thf(zip_derived_cl1396, plain,
% 122.49/16.41      (~ (((setukpairinjL2) =>
% 122.49/16.41           (((setukpairinjL) =>
% 122.49/16.41             (((setukpairinjR11) =>
% 122.49/16.41               (((setukpairinjR12) =>
% 122.49/16.41                 (((setukpairinjR1) =>
% 122.49/16.41                   (((upairequniteq) =>
% 122.49/16.41                     (((setukpairinjR2) =>
% 122.49/16.41                       (((setukpairinjR) =>
% 122.49/16.41                         (((ksndsingleton) =>
% 122.49/16.41                           (((ksndpairEq) =>
% 122.49/16.41                             (((kpairsurjEq) =>
% 122.49/16.41                               (((cartprodsndin) =>
% 122.49/16.41                                 (((cartprodpairmemEL) =>
% 122.49/16.41                                   (((cartprodpairmemER) =>
% 122.49/16.41                                     (((cartprodmempaircEq) =>
% 122.49/16.41                                       (((cartprodfstpairEq) =>
% 122.49/16.41                                         (((cartprodsndpairEq) =>
% 122.49/16.41                                           (((cartprodpairsurjEq) =>
% 122.49/16.41                                             (((dpsetconstrI) =>
% 122.49/16.41                                               (((dpsetconstrSub) =>
% 122.49/16.41                                                 (((setOfPairsIsBReln) =>
% 122.49/16.41                                                   (((dpsetconstrERa) =>
% 122.49/16.41                                                     (((dpsetconstrEL1) =>
% 122.49/16.41                                                       (((dpsetconstrEL2) =>
% 122.49/16.41                                                         (((dpsetconstrER) =>
% 122.49/16.41                                                           (((funcImageSingleton) =>
% 122.49/16.41                                                             (((apProp) =>
% 122.49/16.41                                                               (((app) =>
% 122.49/16.41                                                                 (((infuncsetfunc) =>
% 122.49/16.41                                                                   (((ap2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcinfuncset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1382])).
% 122.49/16.41  thf(zip_derived_cl1409, plain,
% 122.49/16.41      (~ (((setukpairinjL) =>
% 122.49/16.41           (((setukpairinjR11) =>
% 122.49/16.41             (((setukpairinjR12) =>
% 122.49/16.41               (((setukpairinjR1) =>
% 122.49/16.41                 (((upairequniteq) =>
% 122.49/16.41                   (((setukpairinjR2) =>
% 122.49/16.41                     (((setukpairinjR) =>
% 122.49/16.41                       (((ksndsingleton) =>
% 122.49/16.41                         (((ksndpairEq) =>
% 122.49/16.41                           (((kpairsurjEq) =>
% 122.49/16.41                             (((cartprodsndin) =>
% 122.49/16.41                               (((cartprodpairmemEL) =>
% 122.49/16.41                                 (((cartprodpairmemER) =>
% 122.49/16.41                                   (((cartprodmempaircEq) =>
% 122.49/16.41                                     (((cartprodfstpairEq) =>
% 122.49/16.41                                       (((cartprodsndpairEq) =>
% 122.49/16.41                                         (((cartprodpairsurjEq) =>
% 122.49/16.41                                           (((dpsetconstrI) =>
% 122.49/16.41                                             (((dpsetconstrSub) =>
% 122.49/16.41                                               (((setOfPairsIsBReln) =>
% 122.49/16.41                                                 (((dpsetconstrERa) =>
% 122.49/16.41                                                   (((dpsetconstrEL1) =>
% 122.49/16.41                                                     (((dpsetconstrEL2) =>
% 122.49/16.41                                                       (((dpsetconstrER) =>
% 122.49/16.41                                                         (((funcImageSingleton) =>
% 122.49/16.41                                                           (((apProp) =>
% 122.49/16.41                                                             (((app) =>
% 122.49/16.41                                                               (((infuncsetfunc) =>
% 122.49/16.41                                                                 (((ap2p) =>
% 122.49/16.41                                                                   (((funcinfuncset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1396])).
% 122.49/16.41  thf(zip_derived_cl1425, plain,
% 122.49/16.41      (~ (((setukpairinjR11) =>
% 122.49/16.41           (((setukpairinjR12) =>
% 122.49/16.41             (((setukpairinjR1) =>
% 122.49/16.41               (((upairequniteq) =>
% 122.49/16.41                 (((setukpairinjR2) =>
% 122.49/16.41                   (((setukpairinjR) =>
% 122.49/16.41                     (((ksndsingleton) =>
% 122.49/16.41                       (((ksndpairEq) =>
% 122.49/16.41                         (((kpairsurjEq) =>
% 122.49/16.41                           (((cartprodsndin) =>
% 122.49/16.41                             (((cartprodpairmemEL) =>
% 122.49/16.41                               (((cartprodpairmemER) =>
% 122.49/16.41                                 (((cartprodmempaircEq) =>
% 122.49/16.41                                   (((cartprodfstpairEq) =>
% 122.49/16.41                                     (((cartprodsndpairEq) =>
% 122.49/16.41                                       (((cartprodpairsurjEq) =>
% 122.49/16.41                                         (((dpsetconstrI) =>
% 122.49/16.41                                           (((dpsetconstrSub) =>
% 122.49/16.41                                             (((setOfPairsIsBReln) =>
% 122.49/16.41                                               (((dpsetconstrERa) =>
% 122.49/16.41                                                 (((dpsetconstrEL1) =>
% 122.49/16.41                                                   (((dpsetconstrEL2) =>
% 122.49/16.41                                                     (((dpsetconstrER) =>
% 122.49/16.41                                                       (((funcImageSingleton) =>
% 122.49/16.41                                                         (((apProp) =>
% 122.49/16.41                                                           (((app) =>
% 122.49/16.41                                                             (((infuncsetfunc) =>
% 122.49/16.41                                                               (((ap2p) =>
% 122.49/16.41                                                                 (((funcinfuncset) =>
% 122.49/16.41                                                                   (((lamProp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lamp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1409])).
% 122.49/16.41  thf(zip_derived_cl1440, plain,
% 122.49/16.41      (~ (((setukpairinjR12) =>
% 122.49/16.41           (((setukpairinjR1) =>
% 122.49/16.41             (((upairequniteq) =>
% 122.49/16.41               (((setukpairinjR2) =>
% 122.49/16.41                 (((setukpairinjR) =>
% 122.49/16.41                   (((ksndsingleton) =>
% 122.49/16.41                     (((ksndpairEq) =>
% 122.49/16.41                       (((kpairsurjEq) =>
% 122.49/16.41                         (((cartprodsndin) =>
% 122.49/16.41                           (((cartprodpairmemEL) =>
% 122.49/16.41                             (((cartprodpairmemER) =>
% 122.49/16.41                               (((cartprodmempaircEq) =>
% 122.49/16.41                                 (((cartprodfstpairEq) =>
% 122.49/16.41                                   (((cartprodsndpairEq) =>
% 122.49/16.41                                     (((cartprodpairsurjEq) =>
% 122.49/16.41                                       (((dpsetconstrI) =>
% 122.49/16.41                                         (((dpsetconstrSub) =>
% 122.49/16.41                                           (((setOfPairsIsBReln) =>
% 122.49/16.41                                             (((dpsetconstrERa) =>
% 122.49/16.41                                               (((dpsetconstrEL1) =>
% 122.49/16.41                                                 (((dpsetconstrEL2) =>
% 122.49/16.41                                                   (((dpsetconstrER) =>
% 122.49/16.41                                                     (((funcImageSingleton) =>
% 122.49/16.41                                                       (((apProp) =>
% 122.49/16.41                                                         (((app) =>
% 122.49/16.41                                                           (((infuncsetfunc) =>
% 122.49/16.41                                                             (((ap2p) =>
% 122.49/16.41                                                               (((funcinfuncset) =>
% 122.49/16.41                                                                 (((lamProp) =>
% 122.49/16.41                                                                   (((lamp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1425])).
% 122.49/16.41  thf(zip_derived_cl1453, plain,
% 122.49/16.41      (~ (((setukpairinjR1) =>
% 122.49/16.41           (((upairequniteq) =>
% 122.49/16.41             (((setukpairinjR2) =>
% 122.49/16.41               (((setukpairinjR) =>
% 122.49/16.41                 (((ksndsingleton) =>
% 122.49/16.41                   (((ksndpairEq) =>
% 122.49/16.41                     (((kpairsurjEq) =>
% 122.49/16.41                       (((cartprodsndin) =>
% 122.49/16.41                         (((cartprodpairmemEL) =>
% 122.49/16.41                           (((cartprodpairmemER) =>
% 122.49/16.41                             (((cartprodmempaircEq) =>
% 122.49/16.41                               (((cartprodfstpairEq) =>
% 122.49/16.41                                 (((cartprodsndpairEq) =>
% 122.49/16.41                                   (((cartprodpairsurjEq) =>
% 122.49/16.41                                     (((dpsetconstrI) =>
% 122.49/16.41                                       (((dpsetconstrSub) =>
% 122.49/16.41                                         (((setOfPairsIsBReln) =>
% 122.49/16.41                                           (((dpsetconstrERa) =>
% 122.49/16.41                                             (((dpsetconstrEL1) =>
% 122.49/16.41                                               (((dpsetconstrEL2) =>
% 122.49/16.41                                                 (((dpsetconstrER) =>
% 122.49/16.41                                                   (((funcImageSingleton) =>
% 122.49/16.41                                                     (((apProp) =>
% 122.49/16.41                                                       (((app) =>
% 122.49/16.41                                                         (((infuncsetfunc) =>
% 122.49/16.41                                                           (((ap2p) =>
% 122.49/16.41                                                             (((funcinfuncset) =>
% 122.49/16.41                                                               (((lamProp) =>
% 122.49/16.41                                                                 (((lamp) =>
% 122.49/16.41                                                                   (((lam2p) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1440])).
% 122.49/16.41  thf(zip_derived_cl1465, plain,
% 122.49/16.41      (~ (((upairequniteq) =>
% 122.49/16.41           (((setukpairinjR2) =>
% 122.49/16.41             (((setukpairinjR) =>
% 122.49/16.41               (((ksndsingleton) =>
% 122.49/16.41                 (((ksndpairEq) =>
% 122.49/16.41                   (((kpairsurjEq) =>
% 122.49/16.41                     (((cartprodsndin) =>
% 122.49/16.41                       (((cartprodpairmemEL) =>
% 122.49/16.41                         (((cartprodpairmemER) =>
% 122.49/16.41                           (((cartprodmempaircEq) =>
% 122.49/16.41                             (((cartprodfstpairEq) =>
% 122.49/16.41                               (((cartprodsndpairEq) =>
% 122.49/16.41                                 (((cartprodpairsurjEq) =>
% 122.49/16.41                                   (((dpsetconstrI) =>
% 122.49/16.41                                     (((dpsetconstrSub) =>
% 122.49/16.41                                       (((setOfPairsIsBReln) =>
% 122.49/16.41                                         (((dpsetconstrERa) =>
% 122.49/16.41                                           (((dpsetconstrEL1) =>
% 122.49/16.41                                             (((dpsetconstrEL2) =>
% 122.49/16.41                                               (((dpsetconstrER) =>
% 122.49/16.41                                                 (((funcImageSingleton) =>
% 122.49/16.41                                                   (((apProp) =>
% 122.49/16.41                                                     (((app) =>
% 122.49/16.41                                                       (((infuncsetfunc) =>
% 122.49/16.41                                                         (((ap2p) =>
% 122.49/16.41                                                           (((funcinfuncset) =>
% 122.49/16.41                                                             (((lamProp) =>
% 122.49/16.41                                                               (((lamp) =>
% 122.49/16.41                                                                 (((lam2p) =>
% 122.49/16.41                                                                   (((brelnall1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y1 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (!!) @ (
% 122.49/16.41                                                                      ^[Y2 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y2 @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ 
% 122.49/16.41                                                                      Y2) =>
% 122.49/16.41                                                                      (in @ 
% 122.49/16.41                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.41      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1453])).
% 122.49/16.41  thf(zip_derived_cl1475, plain,
% 122.49/16.41      (~ (((setukpairinjR2) =>
% 122.49/16.41           (((setukpairinjR) =>
% 122.49/16.41             (((ksndsingleton) =>
% 122.49/16.41               (((ksndpairEq) =>
% 122.49/16.41                 (((kpairsurjEq) =>
% 122.49/16.41                   (((cartprodsndin) =>
% 122.49/16.41                     (((cartprodpairmemEL) =>
% 122.49/16.41                       (((cartprodpairmemER) =>
% 122.49/16.41                         (((cartprodmempaircEq) =>
% 122.49/16.41                           (((cartprodfstpairEq) =>
% 122.49/16.41                             (((cartprodsndpairEq) =>
% 122.49/16.41                               (((cartprodpairsurjEq) =>
% 122.49/16.41                                 (((dpsetconstrI) =>
% 122.49/16.41                                   (((dpsetconstrSub) =>
% 122.49/16.41                                     (((setOfPairsIsBReln) =>
% 122.49/16.41                                       (((dpsetconstrERa) =>
% 122.49/16.41                                         (((dpsetconstrEL1) =>
% 122.49/16.41                                           (((dpsetconstrEL2) =>
% 122.49/16.41                                             (((dpsetconstrER) =>
% 122.49/16.41                                               (((funcImageSingleton) =>
% 122.49/16.41                                                 (((apProp) =>
% 122.49/16.41                                                   (((app) =>
% 122.49/16.41                                                     (((infuncsetfunc) =>
% 122.49/16.41                                                       (((ap2p) =>
% 122.49/16.41                                                         (((funcinfuncset) =>
% 122.49/16.41                                                           (((lamProp) =>
% 122.49/16.41                                                             (((lamp) =>
% 122.49/16.41                                                               (((lam2p) =>
% 122.49/16.41                                                                 (((brelnall1) =>
% 122.49/16.41                                                                   (((brelnall2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ex1E2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcextLem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcGraphProp4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (funcext2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ap2apEq2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (lam2lamEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (beta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eta2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalseProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueProp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifSingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ifp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (theeq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrue) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iffalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (iftrueorfalse) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setminusT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementT_lem) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setextT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subsetTI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (powersetTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTELcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintersectTERcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contrasubsetT3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementI1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementE1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementSub2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (doubleComplementEq) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTnotintersectT) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementImpComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (contraSubsetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementTcontraSubset) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTILcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTIRcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binunionTEcontra) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2a) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2b) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (demorgan2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule0) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz13rule4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_3) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_4) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz1_5) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1SetBreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (choice2fnsingleton) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1all1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (subbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (eqbreln1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1invE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1compEex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionprop) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIL) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionIR) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionI) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionE) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionEcases) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (breln1unionCommutes) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2W) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2A) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (woz2B) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Ex1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1Equiv) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1E) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (image1I) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (injFuncSetFuncInj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (leftInvIsSurj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (surjCantorThm) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (foundation2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (notinself2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSp) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (omegaSclos) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peano0notS) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (peanoSinj) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (binintTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (transitivesetOp2) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (setunionTransitive) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (ordinalMinLem1) =>
% 122.49/16.41                                                                     ((
% 122.49/16.41                                                                     (!!) @ (
% 122.49/16.41                                                                     ^[Y0 : $i]:
% 122.49/16.41                                                                      ((
% 122.49/16.41                                                                      (ordinal @ 
% 122.49/16.41                                                                      Y0) =>
% 122.49/16.41                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1465])).
% 122.49/16.42  thf(zip_derived_cl1485, plain,
% 122.49/16.42      (~ (((setukpairinjR) =>
% 122.49/16.42           (((ksndsingleton) =>
% 122.49/16.42             (((ksndpairEq) =>
% 122.49/16.42               (((kpairsurjEq) =>
% 122.49/16.42                 (((cartprodsndin) =>
% 122.49/16.42                   (((cartprodpairmemEL) =>
% 122.49/16.42                     (((cartprodpairmemER) =>
% 122.49/16.42                       (((cartprodmempaircEq) =>
% 122.49/16.42                         (((cartprodfstpairEq) =>
% 122.49/16.42                           (((cartprodsndpairEq) =>
% 122.49/16.42                             (((cartprodpairsurjEq) =>
% 122.49/16.42                               (((dpsetconstrI) =>
% 122.49/16.42                                 (((dpsetconstrSub) =>
% 122.49/16.42                                   (((setOfPairsIsBReln) =>
% 122.49/16.42                                     (((dpsetconstrERa) =>
% 122.49/16.42                                       (((dpsetconstrEL1) =>
% 122.49/16.42                                         (((dpsetconstrEL2) =>
% 122.49/16.42                                           (((dpsetconstrER) =>
% 122.49/16.42                                             (((funcImageSingleton) =>
% 122.49/16.42                                               (((apProp) =>
% 122.49/16.42                                                 (((app) =>
% 122.49/16.42                                                   (((infuncsetfunc) =>
% 122.49/16.42                                                     (((ap2p) =>
% 122.49/16.42                                                       (((funcinfuncset) =>
% 122.49/16.42                                                         (((lamProp) =>
% 122.49/16.42                                                           (((lamp) =>
% 122.49/16.42                                                             (((lam2p) =>
% 122.49/16.42                                                               (((brelnall1) =>
% 122.49/16.42                                                                 (((brelnall2) =>
% 122.49/16.42                                                                   (((ex1E2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcGraphProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcGraphProp3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcGraphProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcextLem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcGraphProp4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1475])).
% 122.49/16.42  thf(zip_derived_cl1495, plain,
% 122.49/16.42      (~ (((ksndsingleton) =>
% 122.49/16.42           (((ksndpairEq) =>
% 122.49/16.42             (((kpairsurjEq) =>
% 122.49/16.42               (((cartprodsndin) =>
% 122.49/16.42                 (((cartprodpairmemEL) =>
% 122.49/16.42                   (((cartprodpairmemER) =>
% 122.49/16.42                     (((cartprodmempaircEq) =>
% 122.49/16.42                       (((cartprodfstpairEq) =>
% 122.49/16.42                         (((cartprodsndpairEq) =>
% 122.49/16.42                           (((cartprodpairsurjEq) =>
% 122.49/16.42                             (((dpsetconstrI) =>
% 122.49/16.42                               (((dpsetconstrSub) =>
% 122.49/16.42                                 (((setOfPairsIsBReln) =>
% 122.49/16.42                                   (((dpsetconstrERa) =>
% 122.49/16.42                                     (((dpsetconstrEL1) =>
% 122.49/16.42                                       (((dpsetconstrEL2) =>
% 122.49/16.42                                         (((dpsetconstrER) =>
% 122.49/16.42                                           (((funcImageSingleton) =>
% 122.49/16.42                                             (((apProp) =>
% 122.49/16.42                                               (((app) =>
% 122.49/16.42                                                 (((infuncsetfunc) =>
% 122.49/16.42                                                   (((ap2p) =>
% 122.49/16.42                                                     (((funcinfuncset) =>
% 122.49/16.42                                                       (((lamProp) =>
% 122.49/16.42                                                         (((lamp) =>
% 122.49/16.42                                                           (((lam2p) =>
% 122.49/16.42                                                             (((brelnall1) =>
% 122.49/16.42                                                               (((brelnall2) =>
% 122.49/16.42                                                                 (((ex1E2) =>
% 122.49/16.42                                                                   (((funcGraphProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcGraphProp3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcGraphProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcextLem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcGraphProp4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1485])).
% 122.49/16.42  thf(zip_derived_cl1504, plain,
% 122.49/16.42      (~ (((ksndpairEq) =>
% 122.49/16.42           (((kpairsurjEq) =>
% 122.49/16.42             (((cartprodsndin) =>
% 122.49/16.42               (((cartprodpairmemEL) =>
% 122.49/16.42                 (((cartprodpairmemER) =>
% 122.49/16.42                   (((cartprodmempaircEq) =>
% 122.49/16.42                     (((cartprodfstpairEq) =>
% 122.49/16.42                       (((cartprodsndpairEq) =>
% 122.49/16.42                         (((cartprodpairsurjEq) =>
% 122.49/16.42                           (((dpsetconstrI) =>
% 122.49/16.42                             (((dpsetconstrSub) =>
% 122.49/16.42                               (((setOfPairsIsBReln) =>
% 122.49/16.42                                 (((dpsetconstrERa) =>
% 122.49/16.42                                   (((dpsetconstrEL1) =>
% 122.49/16.42                                     (((dpsetconstrEL2) =>
% 122.49/16.42                                       (((dpsetconstrER) =>
% 122.49/16.42                                         (((funcImageSingleton) =>
% 122.49/16.42                                           (((apProp) =>
% 122.49/16.42                                             (((app) =>
% 122.49/16.42                                               (((infuncsetfunc) =>
% 122.49/16.42                                                 (((ap2p) =>
% 122.49/16.42                                                   (((funcinfuncset) =>
% 122.49/16.42                                                     (((lamProp) =>
% 122.49/16.42                                                       (((lamp) =>
% 122.49/16.42                                                         (((lam2p) =>
% 122.49/16.42                                                           (((brelnall1) =>
% 122.49/16.42                                                             (((brelnall2) =>
% 122.49/16.42                                                               (((ex1E2) =>
% 122.49/16.42                                                                 (((funcGraphProp1) =>
% 122.49/16.42                                                                   (((funcGraphProp3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcGraphProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcextLem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcGraphProp4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1495])).
% 122.49/16.42  thf(zip_derived_cl1511, plain,
% 122.49/16.42      (~ (((kpairsurjEq) =>
% 122.49/16.42           (((cartprodsndin) =>
% 122.49/16.42             (((cartprodpairmemEL) =>
% 122.49/16.42               (((cartprodpairmemER) =>
% 122.49/16.42                 (((cartprodmempaircEq) =>
% 122.49/16.42                   (((cartprodfstpairEq) =>
% 122.49/16.42                     (((cartprodsndpairEq) =>
% 122.49/16.42                       (((cartprodpairsurjEq) =>
% 122.49/16.42                         (((dpsetconstrI) =>
% 122.49/16.42                           (((dpsetconstrSub) =>
% 122.49/16.42                             (((setOfPairsIsBReln) =>
% 122.49/16.42                               (((dpsetconstrERa) =>
% 122.49/16.42                                 (((dpsetconstrEL1) =>
% 122.49/16.42                                   (((dpsetconstrEL2) =>
% 122.49/16.42                                     (((dpsetconstrER) =>
% 122.49/16.42                                       (((funcImageSingleton) =>
% 122.49/16.42                                         (((apProp) =>
% 122.49/16.42                                           (((app) =>
% 122.49/16.42                                             (((infuncsetfunc) =>
% 122.49/16.42                                               (((ap2p) =>
% 122.49/16.42                                                 (((funcinfuncset) =>
% 122.49/16.42                                                   (((lamProp) =>
% 122.49/16.42                                                     (((lamp) =>
% 122.49/16.42                                                       (((lam2p) =>
% 122.49/16.42                                                         (((brelnall1) =>
% 122.49/16.42                                                           (((brelnall2) =>
% 122.49/16.42                                                             (((ex1E2) =>
% 122.49/16.42                                                               (((funcGraphProp1) =>
% 122.49/16.42                                                                 (((funcGraphProp3) =>
% 122.49/16.42                                                                   (((funcGraphProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcextLem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcGraphProp4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1504])).
% 122.49/16.42  thf(zip_derived_cl1519, plain,
% 122.49/16.42      (~ (((cartprodsndin) =>
% 122.49/16.42           (((cartprodpairmemEL) =>
% 122.49/16.42             (((cartprodpairmemER) =>
% 122.49/16.42               (((cartprodmempaircEq) =>
% 122.49/16.42                 (((cartprodfstpairEq) =>
% 122.49/16.42                   (((cartprodsndpairEq) =>
% 122.49/16.42                     (((cartprodpairsurjEq) =>
% 122.49/16.42                       (((dpsetconstrI) =>
% 122.49/16.42                         (((dpsetconstrSub) =>
% 122.49/16.42                           (((setOfPairsIsBReln) =>
% 122.49/16.42                             (((dpsetconstrERa) =>
% 122.49/16.42                               (((dpsetconstrEL1) =>
% 122.49/16.42                                 (((dpsetconstrEL2) =>
% 122.49/16.42                                   (((dpsetconstrER) =>
% 122.49/16.42                                     (((funcImageSingleton) =>
% 122.49/16.42                                       (((apProp) =>
% 122.49/16.42                                         (((app) =>
% 122.49/16.42                                           (((infuncsetfunc) =>
% 122.49/16.42                                             (((ap2p) =>
% 122.49/16.42                                               (((funcinfuncset) =>
% 122.49/16.42                                                 (((lamProp) =>
% 122.49/16.42                                                   (((lamp) =>
% 122.49/16.42                                                     (((lam2p) =>
% 122.49/16.42                                                       (((brelnall1) =>
% 122.49/16.42                                                         (((brelnall2) =>
% 122.49/16.42                                                           (((ex1E2) =>
% 122.49/16.42                                                             (((funcGraphProp1) =>
% 122.49/16.42                                                               (((funcGraphProp3) =>
% 122.49/16.42                                                                 (((funcGraphProp2) =>
% 122.49/16.42                                                                   (((funcextLem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcGraphProp4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1511])).
% 122.49/16.42  thf(zip_derived_cl1529, plain,
% 122.49/16.42      (~ (((cartprodpairmemEL) =>
% 122.49/16.42           (((cartprodpairmemER) =>
% 122.49/16.42             (((cartprodmempaircEq) =>
% 122.49/16.42               (((cartprodfstpairEq) =>
% 122.49/16.42                 (((cartprodsndpairEq) =>
% 122.49/16.42                   (((cartprodpairsurjEq) =>
% 122.49/16.42                     (((dpsetconstrI) =>
% 122.49/16.42                       (((dpsetconstrSub) =>
% 122.49/16.42                         (((setOfPairsIsBReln) =>
% 122.49/16.42                           (((dpsetconstrERa) =>
% 122.49/16.42                             (((dpsetconstrEL1) =>
% 122.49/16.42                               (((dpsetconstrEL2) =>
% 122.49/16.42                                 (((dpsetconstrER) =>
% 122.49/16.42                                   (((funcImageSingleton) =>
% 122.49/16.42                                     (((apProp) =>
% 122.49/16.42                                       (((app) =>
% 122.49/16.42                                         (((infuncsetfunc) =>
% 122.49/16.42                                           (((ap2p) =>
% 122.49/16.42                                             (((funcinfuncset) =>
% 122.49/16.42                                               (((lamProp) =>
% 122.49/16.42                                                 (((lamp) =>
% 122.49/16.42                                                   (((lam2p) =>
% 122.49/16.42                                                     (((brelnall1) =>
% 122.49/16.42                                                       (((brelnall2) =>
% 122.49/16.42                                                         (((ex1E2) =>
% 122.49/16.42                                                           (((funcGraphProp1) =>
% 122.49/16.42                                                             (((funcGraphProp3) =>
% 122.49/16.42                                                               (((funcGraphProp2) =>
% 122.49/16.42                                                                 (((funcextLem) =>
% 122.49/16.42                                                                   (((funcGraphProp4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1519])).
% 122.49/16.42  thf(zip_derived_cl1538, plain,
% 122.49/16.42      (~ (((cartprodpairmemER) =>
% 122.49/16.42           (((cartprodmempaircEq) =>
% 122.49/16.42             (((cartprodfstpairEq) =>
% 122.49/16.42               (((cartprodsndpairEq) =>
% 122.49/16.42                 (((cartprodpairsurjEq) =>
% 122.49/16.42                   (((dpsetconstrI) =>
% 122.49/16.42                     (((dpsetconstrSub) =>
% 122.49/16.42                       (((setOfPairsIsBReln) =>
% 122.49/16.42                         (((dpsetconstrERa) =>
% 122.49/16.42                           (((dpsetconstrEL1) =>
% 122.49/16.42                             (((dpsetconstrEL2) =>
% 122.49/16.42                               (((dpsetconstrER) =>
% 122.49/16.42                                 (((funcImageSingleton) =>
% 122.49/16.42                                   (((apProp) =>
% 122.49/16.42                                     (((app) =>
% 122.49/16.42                                       (((infuncsetfunc) =>
% 122.49/16.42                                         (((ap2p) =>
% 122.49/16.42                                           (((funcinfuncset) =>
% 122.49/16.42                                             (((lamProp) =>
% 122.49/16.42                                               (((lamp) =>
% 122.49/16.42                                                 (((lam2p) =>
% 122.49/16.42                                                   (((brelnall1) =>
% 122.49/16.42                                                     (((brelnall2) =>
% 122.49/16.42                                                       (((ex1E2) =>
% 122.49/16.42                                                         (((funcGraphProp1) =>
% 122.49/16.42                                                           (((funcGraphProp3) =>
% 122.49/16.42                                                             (((funcGraphProp2) =>
% 122.49/16.42                                                               (((funcextLem) =>
% 122.49/16.42                                                                 (((funcGraphProp4) =>
% 122.49/16.42                                                                   (((subbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1529])).
% 122.49/16.42  thf(zip_derived_cl1546, plain,
% 122.49/16.42      (~ (((cartprodmempaircEq) =>
% 122.49/16.42           (((cartprodfstpairEq) =>
% 122.49/16.42             (((cartprodsndpairEq) =>
% 122.49/16.42               (((cartprodpairsurjEq) =>
% 122.49/16.42                 (((dpsetconstrI) =>
% 122.49/16.42                   (((dpsetconstrSub) =>
% 122.49/16.42                     (((setOfPairsIsBReln) =>
% 122.49/16.42                       (((dpsetconstrERa) =>
% 122.49/16.42                         (((dpsetconstrEL1) =>
% 122.49/16.42                           (((dpsetconstrEL2) =>
% 122.49/16.42                             (((dpsetconstrER) =>
% 122.49/16.42                               (((funcImageSingleton) =>
% 122.49/16.42                                 (((apProp) =>
% 122.49/16.42                                   (((app) =>
% 122.49/16.42                                     (((infuncsetfunc) =>
% 122.49/16.42                                       (((ap2p) =>
% 122.49/16.42                                         (((funcinfuncset) =>
% 122.49/16.42                                           (((lamProp) =>
% 122.49/16.42                                             (((lamp) =>
% 122.49/16.42                                               (((lam2p) =>
% 122.49/16.42                                                 (((brelnall1) =>
% 122.49/16.42                                                   (((brelnall2) =>
% 122.49/16.42                                                     (((ex1E2) =>
% 122.49/16.42                                                       (((funcGraphProp1) =>
% 122.49/16.42                                                         (((funcGraphProp3) =>
% 122.49/16.42                                                           (((funcGraphProp2) =>
% 122.49/16.42                                                             (((funcextLem) =>
% 122.49/16.42                                                               (((funcGraphProp4) =>
% 122.49/16.42                                                                 (((subbreln) =>
% 122.49/16.42                                                                   (((eqbreln) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1538])).
% 122.49/16.42  thf(zip_derived_cl1553, plain,
% 122.49/16.42      (~ (((cartprodfstpairEq) =>
% 122.49/16.42           (((cartprodsndpairEq) =>
% 122.49/16.42             (((cartprodpairsurjEq) =>
% 122.49/16.42               (((dpsetconstrI) =>
% 122.49/16.42                 (((dpsetconstrSub) =>
% 122.49/16.42                   (((setOfPairsIsBReln) =>
% 122.49/16.42                     (((dpsetconstrERa) =>
% 122.49/16.42                       (((dpsetconstrEL1) =>
% 122.49/16.42                         (((dpsetconstrEL2) =>
% 122.49/16.42                           (((dpsetconstrER) =>
% 122.49/16.42                             (((funcImageSingleton) =>
% 122.49/16.42                               (((apProp) =>
% 122.49/16.42                                 (((app) =>
% 122.49/16.42                                   (((infuncsetfunc) =>
% 122.49/16.42                                     (((ap2p) =>
% 122.49/16.42                                       (((funcinfuncset) =>
% 122.49/16.42                                         (((lamProp) =>
% 122.49/16.42                                           (((lamp) =>
% 122.49/16.42                                             (((lam2p) =>
% 122.49/16.42                                               (((brelnall1) =>
% 122.49/16.42                                                 (((brelnall2) =>
% 122.49/16.42                                                   (((ex1E2) =>
% 122.49/16.42                                                     (((funcGraphProp1) =>
% 122.49/16.42                                                       (((funcGraphProp3) =>
% 122.49/16.42                                                         (((funcGraphProp2) =>
% 122.49/16.42                                                           (((funcextLem) =>
% 122.49/16.42                                                             (((funcGraphProp4) =>
% 122.49/16.42                                                               (((subbreln) =>
% 122.49/16.42                                                                 (((eqbreln) =>
% 122.49/16.42                                                                   (((funcext) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (funcext2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1546])).
% 122.49/16.42  thf(zip_derived_cl1559, plain,
% 122.49/16.42      (~ (((cartprodsndpairEq) =>
% 122.49/16.42           (((cartprodpairsurjEq) =>
% 122.49/16.42             (((dpsetconstrI) =>
% 122.49/16.42               (((dpsetconstrSub) =>
% 122.49/16.42                 (((setOfPairsIsBReln) =>
% 122.49/16.42                   (((dpsetconstrERa) =>
% 122.49/16.42                     (((dpsetconstrEL1) =>
% 122.49/16.42                       (((dpsetconstrEL2) =>
% 122.49/16.42                         (((dpsetconstrER) =>
% 122.49/16.42                           (((funcImageSingleton) =>
% 122.49/16.42                             (((apProp) =>
% 122.49/16.42                               (((app) =>
% 122.49/16.42                                 (((infuncsetfunc) =>
% 122.49/16.42                                   (((ap2p) =>
% 122.49/16.42                                     (((funcinfuncset) =>
% 122.49/16.42                                       (((lamProp) =>
% 122.49/16.42                                         (((lamp) =>
% 122.49/16.42                                           (((lam2p) =>
% 122.49/16.42                                             (((brelnall1) =>
% 122.49/16.42                                               (((brelnall2) =>
% 122.49/16.42                                                 (((ex1E2) =>
% 122.49/16.42                                                   (((funcGraphProp1) =>
% 122.49/16.42                                                     (((funcGraphProp3) =>
% 122.49/16.42                                                       (((funcGraphProp2) =>
% 122.49/16.42                                                         (((funcextLem) =>
% 122.49/16.42                                                           (((funcGraphProp4) =>
% 122.49/16.42                                                             (((subbreln) =>
% 122.49/16.42                                                               (((eqbreln) =>
% 122.49/16.42                                                                 (((funcext) =>
% 122.49/16.42                                                                   (((funcext2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1553])).
% 122.49/16.42  thf(zip_derived_cl1566, plain,
% 122.49/16.42      (~ (((cartprodpairsurjEq) =>
% 122.49/16.42           (((dpsetconstrI) =>
% 122.49/16.42             (((dpsetconstrSub) =>
% 122.49/16.42               (((setOfPairsIsBReln) =>
% 122.49/16.42                 (((dpsetconstrERa) =>
% 122.49/16.42                   (((dpsetconstrEL1) =>
% 122.49/16.42                     (((dpsetconstrEL2) =>
% 122.49/16.42                       (((dpsetconstrER) =>
% 122.49/16.42                         (((funcImageSingleton) =>
% 122.49/16.42                           (((apProp) =>
% 122.49/16.42                             (((app) =>
% 122.49/16.42                               (((infuncsetfunc) =>
% 122.49/16.42                                 (((ap2p) =>
% 122.49/16.42                                   (((funcinfuncset) =>
% 122.49/16.42                                     (((lamProp) =>
% 122.49/16.42                                       (((lamp) =>
% 122.49/16.42                                         (((lam2p) =>
% 122.49/16.42                                           (((brelnall1) =>
% 122.49/16.42                                             (((brelnall2) =>
% 122.49/16.42                                               (((ex1E2) =>
% 122.49/16.42                                                 (((funcGraphProp1) =>
% 122.49/16.42                                                   (((funcGraphProp3) =>
% 122.49/16.42                                                     (((funcGraphProp2) =>
% 122.49/16.42                                                       (((funcextLem) =>
% 122.49/16.42                                                         (((funcGraphProp4) =>
% 122.49/16.42                                                           (((subbreln) =>
% 122.49/16.42                                                             (((eqbreln) =>
% 122.49/16.42                                                               (((funcext) =>
% 122.49/16.42                                                                 (((funcext2) =>
% 122.49/16.42                                                                   (((ap2apEq1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ap2apEq2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1559])).
% 122.49/16.42  thf(zip_derived_cl1572, plain,
% 122.49/16.42      (~ (((dpsetconstrI) =>
% 122.49/16.42           (((dpsetconstrSub) =>
% 122.49/16.42             (((setOfPairsIsBReln) =>
% 122.49/16.42               (((dpsetconstrERa) =>
% 122.49/16.42                 (((dpsetconstrEL1) =>
% 122.49/16.42                   (((dpsetconstrEL2) =>
% 122.49/16.42                     (((dpsetconstrER) =>
% 122.49/16.42                       (((funcImageSingleton) =>
% 122.49/16.42                         (((apProp) =>
% 122.49/16.42                           (((app) =>
% 122.49/16.42                             (((infuncsetfunc) =>
% 122.49/16.42                               (((ap2p) =>
% 122.49/16.42                                 (((funcinfuncset) =>
% 122.49/16.42                                   (((lamProp) =>
% 122.49/16.42                                     (((lamp) =>
% 122.49/16.42                                       (((lam2p) =>
% 122.49/16.42                                         (((brelnall1) =>
% 122.49/16.42                                           (((brelnall2) =>
% 122.49/16.42                                             (((ex1E2) =>
% 122.49/16.42                                               (((funcGraphProp1) =>
% 122.49/16.42                                                 (((funcGraphProp3) =>
% 122.49/16.42                                                   (((funcGraphProp2) =>
% 122.49/16.42                                                     (((funcextLem) =>
% 122.49/16.42                                                       (((funcGraphProp4) =>
% 122.49/16.42                                                         (((subbreln) =>
% 122.49/16.42                                                           (((eqbreln) =>
% 122.49/16.42                                                             (((funcext) =>
% 122.49/16.42                                                               (((funcext2) =>
% 122.49/16.42                                                                 (((ap2apEq1) =>
% 122.49/16.42                                                                   (((ap2apEq2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1566])).
% 122.49/16.42  thf(zip_derived_cl1579, plain,
% 122.49/16.42      (~ (((dpsetconstrSub) =>
% 122.49/16.42           (((setOfPairsIsBReln) =>
% 122.49/16.42             (((dpsetconstrERa) =>
% 122.49/16.42               (((dpsetconstrEL1) =>
% 122.49/16.42                 (((dpsetconstrEL2) =>
% 122.49/16.42                   (((dpsetconstrER) =>
% 122.49/16.42                     (((funcImageSingleton) =>
% 122.49/16.42                       (((apProp) =>
% 122.49/16.42                         (((app) =>
% 122.49/16.42                           (((infuncsetfunc) =>
% 122.49/16.42                             (((ap2p) =>
% 122.49/16.42                               (((funcinfuncset) =>
% 122.49/16.42                                 (((lamProp) =>
% 122.49/16.42                                   (((lamp) =>
% 122.49/16.42                                     (((lam2p) =>
% 122.49/16.42                                       (((brelnall1) =>
% 122.49/16.42                                         (((brelnall2) =>
% 122.49/16.42                                           (((ex1E2) =>
% 122.49/16.42                                             (((funcGraphProp1) =>
% 122.49/16.42                                               (((funcGraphProp3) =>
% 122.49/16.42                                                 (((funcGraphProp2) =>
% 122.49/16.42                                                   (((funcextLem) =>
% 122.49/16.42                                                     (((funcGraphProp4) =>
% 122.49/16.42                                                       (((subbreln) =>
% 122.49/16.42                                                         (((eqbreln) =>
% 122.49/16.42                                                           (((funcext) =>
% 122.49/16.42                                                             (((funcext2) =>
% 122.49/16.42                                                               (((ap2apEq1) =>
% 122.49/16.42                                                                 (((ap2apEq2) =>
% 122.49/16.42                                                                   (((beta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1572])).
% 122.49/16.42  thf(zip_derived_cl1586, plain,
% 122.49/16.42      (~ (((setOfPairsIsBReln) =>
% 122.49/16.42           (((dpsetconstrERa) =>
% 122.49/16.42             (((dpsetconstrEL1) =>
% 122.49/16.42               (((dpsetconstrEL2) =>
% 122.49/16.42                 (((dpsetconstrER) =>
% 122.49/16.42                   (((funcImageSingleton) =>
% 122.49/16.42                     (((apProp) =>
% 122.49/16.42                       (((app) =>
% 122.49/16.42                         (((infuncsetfunc) =>
% 122.49/16.42                           (((ap2p) =>
% 122.49/16.42                             (((funcinfuncset) =>
% 122.49/16.42                               (((lamProp) =>
% 122.49/16.42                                 (((lamp) =>
% 122.49/16.42                                   (((lam2p) =>
% 122.49/16.42                                     (((brelnall1) =>
% 122.49/16.42                                       (((brelnall2) =>
% 122.49/16.42                                         (((ex1E2) =>
% 122.49/16.42                                           (((funcGraphProp1) =>
% 122.49/16.42                                             (((funcGraphProp3) =>
% 122.49/16.42                                               (((funcGraphProp2) =>
% 122.49/16.42                                                 (((funcextLem) =>
% 122.49/16.42                                                   (((funcGraphProp4) =>
% 122.49/16.42                                                     (((subbreln) =>
% 122.49/16.42                                                       (((eqbreln) =>
% 122.49/16.42                                                         (((funcext) =>
% 122.49/16.42                                                           (((funcext2) =>
% 122.49/16.42                                                             (((ap2apEq1) =>
% 122.49/16.42                                                               (((ap2apEq2) =>
% 122.49/16.42                                                                 (((beta1) =>
% 122.49/16.42                                                                   (((eta1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1579])).
% 122.49/16.42  thf(zip_derived_cl1594, plain,
% 122.49/16.42      (~ (((dpsetconstrERa) =>
% 122.49/16.42           (((dpsetconstrEL1) =>
% 122.49/16.42             (((dpsetconstrEL2) =>
% 122.49/16.42               (((dpsetconstrER) =>
% 122.49/16.42                 (((funcImageSingleton) =>
% 122.49/16.42                   (((apProp) =>
% 122.49/16.42                     (((app) =>
% 122.49/16.42                       (((infuncsetfunc) =>
% 122.49/16.42                         (((ap2p) =>
% 122.49/16.42                           (((funcinfuncset) =>
% 122.49/16.42                             (((lamProp) =>
% 122.49/16.42                               (((lamp) =>
% 122.49/16.42                                 (((lam2p) =>
% 122.49/16.42                                   (((brelnall1) =>
% 122.49/16.42                                     (((brelnall2) =>
% 122.49/16.42                                       (((ex1E2) =>
% 122.49/16.42                                         (((funcGraphProp1) =>
% 122.49/16.42                                           (((funcGraphProp3) =>
% 122.49/16.42                                             (((funcGraphProp2) =>
% 122.49/16.42                                               (((funcextLem) =>
% 122.49/16.42                                                 (((funcGraphProp4) =>
% 122.49/16.42                                                   (((subbreln) =>
% 122.49/16.42                                                     (((eqbreln) =>
% 122.49/16.42                                                       (((funcext) =>
% 122.49/16.42                                                         (((funcext2) =>
% 122.49/16.42                                                           (((ap2apEq1) =>
% 122.49/16.42                                                             (((ap2apEq2) =>
% 122.49/16.42                                                               (((beta1) =>
% 122.49/16.42                                                                 (((eta1) =>
% 122.49/16.42                                                                   (((lam2lamEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1586])).
% 122.49/16.42  thf(zip_derived_cl1603, plain,
% 122.49/16.42      (~ (((dpsetconstrEL1) =>
% 122.49/16.42           (((dpsetconstrEL2) =>
% 122.49/16.42             (((dpsetconstrER) =>
% 122.49/16.42               (((funcImageSingleton) =>
% 122.49/16.42                 (((apProp) =>
% 122.49/16.42                   (((app) =>
% 122.49/16.42                     (((infuncsetfunc) =>
% 122.49/16.42                       (((ap2p) =>
% 122.49/16.42                         (((funcinfuncset) =>
% 122.49/16.42                           (((lamProp) =>
% 122.49/16.42                             (((lamp) =>
% 122.49/16.42                               (((lam2p) =>
% 122.49/16.42                                 (((brelnall1) =>
% 122.49/16.42                                   (((brelnall2) =>
% 122.49/16.42                                     (((ex1E2) =>
% 122.49/16.42                                       (((funcGraphProp1) =>
% 122.49/16.42                                         (((funcGraphProp3) =>
% 122.49/16.42                                           (((funcGraphProp2) =>
% 122.49/16.42                                             (((funcextLem) =>
% 122.49/16.42                                               (((funcGraphProp4) =>
% 122.49/16.42                                                 (((subbreln) =>
% 122.49/16.42                                                   (((eqbreln) =>
% 122.49/16.42                                                     (((funcext) =>
% 122.49/16.42                                                       (((funcext2) =>
% 122.49/16.42                                                         (((ap2apEq1) =>
% 122.49/16.42                                                           (((ap2apEq2) =>
% 122.49/16.42                                                             (((beta1) =>
% 122.49/16.42                                                               (((eta1) =>
% 122.49/16.42                                                                 (((lam2lamEq) =>
% 122.49/16.42                                                                   (((beta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1594])).
% 122.49/16.42  thf(zip_derived_cl1613, plain,
% 122.49/16.42      (~ (((dpsetconstrEL2) =>
% 122.49/16.42           (((dpsetconstrER) =>
% 122.49/16.42             (((funcImageSingleton) =>
% 122.49/16.42               (((apProp) =>
% 122.49/16.42                 (((app) =>
% 122.49/16.42                   (((infuncsetfunc) =>
% 122.49/16.42                     (((ap2p) =>
% 122.49/16.42                       (((funcinfuncset) =>
% 122.49/16.42                         (((lamProp) =>
% 122.49/16.42                           (((lamp) =>
% 122.49/16.42                             (((lam2p) =>
% 122.49/16.42                               (((brelnall1) =>
% 122.49/16.42                                 (((brelnall2) =>
% 122.49/16.42                                   (((ex1E2) =>
% 122.49/16.42                                     (((funcGraphProp1) =>
% 122.49/16.42                                       (((funcGraphProp3) =>
% 122.49/16.42                                         (((funcGraphProp2) =>
% 122.49/16.42                                           (((funcextLem) =>
% 122.49/16.42                                             (((funcGraphProp4) =>
% 122.49/16.42                                               (((subbreln) =>
% 122.49/16.42                                                 (((eqbreln) =>
% 122.49/16.42                                                   (((funcext) =>
% 122.49/16.42                                                     (((funcext2) =>
% 122.49/16.42                                                       (((ap2apEq1) =>
% 122.49/16.42                                                         (((ap2apEq2) =>
% 122.49/16.42                                                           (((beta1) =>
% 122.49/16.42                                                             (((eta1) =>
% 122.49/16.42                                                               (((lam2lamEq) =>
% 122.49/16.42                                                                 (((beta2) =>
% 122.49/16.42                                                                   (((eta2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementEq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTnotintersectT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementImpComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contraSubsetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTcontraSubset) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTILcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTIRcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionTEcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2a) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2b) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (demorgan2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule0) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz13rule4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_4) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz1_5) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1SetBreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (choice2fnsingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1all1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (eqbreln1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1invE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1compEex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionprop) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIL) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionIR) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionE) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionEcases) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (breln1unionCommutes) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2W) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2A) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (woz2B) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Ex1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1Equiv) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1E) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (image1I) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (injFuncSetFuncInj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (leftInvIsSurj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (surjCantorThm) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (foundation2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (notinself2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (omegaSclos) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peano0notS) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (peanoSinj) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (transitivesetOp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setunionTransitive) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ordinalMinLem1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (!!) @ (
% 122.49/16.42                                                                     ^[Y0 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (ordinal @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y1 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (!!) @ (
% 122.49/16.42                                                                      ^[Y2 : $i]:
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y2 @ 
% 122.49/16.42                                                                      Y0) =>
% 122.49/16.42                                                                      ((
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ 
% 122.49/16.42                                                                      Y2) =>
% 122.49/16.42                                                                      (in @ 
% 122.49/16.42                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.42      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1603])).
% 122.49/16.42  thf(zip_derived_cl1624, plain,
% 122.49/16.42      (~ (((dpsetconstrER) =>
% 122.49/16.42           (((funcImageSingleton) =>
% 122.49/16.42             (((apProp) =>
% 122.49/16.42               (((app) =>
% 122.49/16.42                 (((infuncsetfunc) =>
% 122.49/16.42                   (((ap2p) =>
% 122.49/16.42                     (((funcinfuncset) =>
% 122.49/16.42                       (((lamProp) =>
% 122.49/16.42                         (((lamp) =>
% 122.49/16.42                           (((lam2p) =>
% 122.49/16.42                             (((brelnall1) =>
% 122.49/16.42                               (((brelnall2) =>
% 122.49/16.42                                 (((ex1E2) =>
% 122.49/16.42                                   (((funcGraphProp1) =>
% 122.49/16.42                                     (((funcGraphProp3) =>
% 122.49/16.42                                       (((funcGraphProp2) =>
% 122.49/16.42                                         (((funcextLem) =>
% 122.49/16.42                                           (((funcGraphProp4) =>
% 122.49/16.42                                             (((subbreln) =>
% 122.49/16.42                                               (((eqbreln) =>
% 122.49/16.42                                                 (((funcext) =>
% 122.49/16.42                                                   (((funcext2) =>
% 122.49/16.42                                                     (((ap2apEq1) =>
% 122.49/16.42                                                       (((ap2apEq2) =>
% 122.49/16.42                                                         (((beta1) =>
% 122.49/16.42                                                           (((eta1) =>
% 122.49/16.42                                                             (((lam2lamEq) =>
% 122.49/16.42                                                               (((beta2) =>
% 122.49/16.42                                                                 (((eta2) =>
% 122.49/16.42                                                                   (((iffalseProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalseProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueProp2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifSingleton) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (ifp) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (theeq) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrue) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iffalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (iftrueorfalse) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binunionT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setminusT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementT_lem) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (setextT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (subsetTI) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (powersetTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (complementTE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTELcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (binintersectTERcontra) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT2) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (contrasubsetT3) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementI1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementE1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub1) =>
% 122.49/16.42                                                                     ((
% 122.49/16.42                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1613])).
% 122.49/16.43  thf(zip_derived_cl1633, plain,
% 122.49/16.43      (~ (((funcImageSingleton) =>
% 122.49/16.43           (((apProp) =>
% 122.49/16.43             (((app) =>
% 122.49/16.43               (((infuncsetfunc) =>
% 122.49/16.43                 (((ap2p) =>
% 122.49/16.43                   (((funcinfuncset) =>
% 122.49/16.43                     (((lamProp) =>
% 122.49/16.43                       (((lamp) =>
% 122.49/16.43                         (((lam2p) =>
% 122.49/16.43                           (((brelnall1) =>
% 122.49/16.43                             (((brelnall2) =>
% 122.49/16.43                               (((ex1E2) =>
% 122.49/16.43                                 (((funcGraphProp1) =>
% 122.49/16.43                                   (((funcGraphProp3) =>
% 122.49/16.43                                     (((funcGraphProp2) =>
% 122.49/16.43                                       (((funcextLem) =>
% 122.49/16.43                                         (((funcGraphProp4) =>
% 122.49/16.43                                           (((subbreln) =>
% 122.49/16.43                                             (((eqbreln) =>
% 122.49/16.43                                               (((funcext) =>
% 122.49/16.43                                                 (((funcext2) =>
% 122.49/16.43                                                   (((ap2apEq1) =>
% 122.49/16.43                                                     (((ap2apEq2) =>
% 122.49/16.43                                                       (((beta1) =>
% 122.49/16.43                                                         (((eta1) =>
% 122.49/16.43                                                           (((lam2lamEq) =>
% 122.49/16.43                                                             (((beta2) =>
% 122.49/16.43                                                               (((eta2) =>
% 122.49/16.43                                                                 (((iffalseProp1) =>
% 122.49/16.43                                                                   (((iffalseProp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrueProp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrueProp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ifSingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ifp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (theeq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrue) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iffalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrueorfalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1624])).
% 122.49/16.43  thf(zip_derived_cl1641, plain,
% 122.49/16.43      (~ (((apProp) =>
% 122.49/16.43           (((app) =>
% 122.49/16.43             (((infuncsetfunc) =>
% 122.49/16.43               (((ap2p) =>
% 122.49/16.43                 (((funcinfuncset) =>
% 122.49/16.43                   (((lamProp) =>
% 122.49/16.43                     (((lamp) =>
% 122.49/16.43                       (((lam2p) =>
% 122.49/16.43                         (((brelnall1) =>
% 122.49/16.43                           (((brelnall2) =>
% 122.49/16.43                             (((ex1E2) =>
% 122.49/16.43                               (((funcGraphProp1) =>
% 122.49/16.43                                 (((funcGraphProp3) =>
% 122.49/16.43                                   (((funcGraphProp2) =>
% 122.49/16.43                                     (((funcextLem) =>
% 122.49/16.43                                       (((funcGraphProp4) =>
% 122.49/16.43                                         (((subbreln) =>
% 122.49/16.43                                           (((eqbreln) =>
% 122.49/16.43                                             (((funcext) =>
% 122.49/16.43                                               (((funcext2) =>
% 122.49/16.43                                                 (((ap2apEq1) =>
% 122.49/16.43                                                   (((ap2apEq2) =>
% 122.49/16.43                                                     (((beta1) =>
% 122.49/16.43                                                       (((eta1) =>
% 122.49/16.43                                                         (((lam2lamEq) =>
% 122.49/16.43                                                           (((beta2) =>
% 122.49/16.43                                                             (((eta2) =>
% 122.49/16.43                                                               (((iffalseProp1) =>
% 122.49/16.43                                                                 (((iffalseProp2) =>
% 122.49/16.43                                                                   (((iftrueProp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrueProp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ifSingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ifp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (theeq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrue) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iffalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrueorfalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1633])).
% 122.49/16.43  thf(zip_derived_cl1650, plain,
% 122.49/16.43      (~ (((app) =>
% 122.49/16.43           (((infuncsetfunc) =>
% 122.49/16.43             (((ap2p) =>
% 122.49/16.43               (((funcinfuncset) =>
% 122.49/16.43                 (((lamProp) =>
% 122.49/16.43                   (((lamp) =>
% 122.49/16.43                     (((lam2p) =>
% 122.49/16.43                       (((brelnall1) =>
% 122.49/16.43                         (((brelnall2) =>
% 122.49/16.43                           (((ex1E2) =>
% 122.49/16.43                             (((funcGraphProp1) =>
% 122.49/16.43                               (((funcGraphProp3) =>
% 122.49/16.43                                 (((funcGraphProp2) =>
% 122.49/16.43                                   (((funcextLem) =>
% 122.49/16.43                                     (((funcGraphProp4) =>
% 122.49/16.43                                       (((subbreln) =>
% 122.49/16.43                                         (((eqbreln) =>
% 122.49/16.43                                           (((funcext) =>
% 122.49/16.43                                             (((funcext2) =>
% 122.49/16.43                                               (((ap2apEq1) =>
% 122.49/16.43                                                 (((ap2apEq2) =>
% 122.49/16.43                                                   (((beta1) =>
% 122.49/16.43                                                     (((eta1) =>
% 122.49/16.43                                                       (((lam2lamEq) =>
% 122.49/16.43                                                         (((beta2) =>
% 122.49/16.43                                                           (((eta2) =>
% 122.49/16.43                                                             (((iffalseProp1) =>
% 122.49/16.43                                                               (((iffalseProp2) =>
% 122.49/16.43                                                                 (((iftrueProp1) =>
% 122.49/16.43                                                                   (((iftrueProp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ifSingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ifp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (theeq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrue) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iffalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrueorfalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1641])).
% 122.49/16.43  thf(zip_derived_cl1659, plain,
% 122.49/16.43      (~ (((infuncsetfunc) =>
% 122.49/16.43           (((ap2p) =>
% 122.49/16.43             (((funcinfuncset) =>
% 122.49/16.43               (((lamProp) =>
% 122.49/16.43                 (((lamp) =>
% 122.49/16.43                   (((lam2p) =>
% 122.49/16.43                     (((brelnall1) =>
% 122.49/16.43                       (((brelnall2) =>
% 122.49/16.43                         (((ex1E2) =>
% 122.49/16.43                           (((funcGraphProp1) =>
% 122.49/16.43                             (((funcGraphProp3) =>
% 122.49/16.43                               (((funcGraphProp2) =>
% 122.49/16.43                                 (((funcextLem) =>
% 122.49/16.43                                   (((funcGraphProp4) =>
% 122.49/16.43                                     (((subbreln) =>
% 122.49/16.43                                       (((eqbreln) =>
% 122.49/16.43                                         (((funcext) =>
% 122.49/16.43                                           (((funcext2) =>
% 122.49/16.43                                             (((ap2apEq1) =>
% 122.49/16.43                                               (((ap2apEq2) =>
% 122.49/16.43                                                 (((beta1) =>
% 122.49/16.43                                                   (((eta1) =>
% 122.49/16.43                                                     (((lam2lamEq) =>
% 122.49/16.43                                                       (((beta2) =>
% 122.49/16.43                                                         (((eta2) =>
% 122.49/16.43                                                           (((iffalseProp1) =>
% 122.49/16.43                                                             (((iffalseProp2) =>
% 122.49/16.43                                                               (((iftrueProp1) =>
% 122.49/16.43                                                                 (((iftrueProp2) =>
% 122.49/16.43                                                                   (((ifSingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ifp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (theeq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrue) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iffalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrueorfalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1650])).
% 122.49/16.43  thf(zip_derived_cl1668, plain,
% 122.49/16.43      (~ (((ap2p) =>
% 122.49/16.43           (((funcinfuncset) =>
% 122.49/16.43             (((lamProp) =>
% 122.49/16.43               (((lamp) =>
% 122.49/16.43                 (((lam2p) =>
% 122.49/16.43                   (((brelnall1) =>
% 122.49/16.43                     (((brelnall2) =>
% 122.49/16.43                       (((ex1E2) =>
% 122.49/16.43                         (((funcGraphProp1) =>
% 122.49/16.43                           (((funcGraphProp3) =>
% 122.49/16.43                             (((funcGraphProp2) =>
% 122.49/16.43                               (((funcextLem) =>
% 122.49/16.43                                 (((funcGraphProp4) =>
% 122.49/16.43                                   (((subbreln) =>
% 122.49/16.43                                     (((eqbreln) =>
% 122.49/16.43                                       (((funcext) =>
% 122.49/16.43                                         (((funcext2) =>
% 122.49/16.43                                           (((ap2apEq1) =>
% 122.49/16.43                                             (((ap2apEq2) =>
% 122.49/16.43                                               (((beta1) =>
% 122.49/16.43                                                 (((eta1) =>
% 122.49/16.43                                                   (((lam2lamEq) =>
% 122.49/16.43                                                     (((beta2) =>
% 122.49/16.43                                                       (((eta2) =>
% 122.49/16.43                                                         (((iffalseProp1) =>
% 122.49/16.43                                                           (((iffalseProp2) =>
% 122.49/16.43                                                             (((iftrueProp1) =>
% 122.49/16.43                                                               (((iftrueProp2) =>
% 122.49/16.43                                                                 (((ifSingleton) =>
% 122.49/16.43                                                                   (((ifp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (theeq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrue) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iffalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrueorfalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1659])).
% 122.49/16.43  thf(zip_derived_cl1678, plain,
% 122.49/16.43      (~ (((funcinfuncset) =>
% 122.49/16.43           (((lamProp) =>
% 122.49/16.43             (((lamp) =>
% 122.49/16.43               (((lam2p) =>
% 122.49/16.43                 (((brelnall1) =>
% 122.49/16.43                   (((brelnall2) =>
% 122.49/16.43                     (((ex1E2) =>
% 122.49/16.43                       (((funcGraphProp1) =>
% 122.49/16.43                         (((funcGraphProp3) =>
% 122.49/16.43                           (((funcGraphProp2) =>
% 122.49/16.43                             (((funcextLem) =>
% 122.49/16.43                               (((funcGraphProp4) =>
% 122.49/16.43                                 (((subbreln) =>
% 122.49/16.43                                   (((eqbreln) =>
% 122.49/16.43                                     (((funcext) =>
% 122.49/16.43                                       (((funcext2) =>
% 122.49/16.43                                         (((ap2apEq1) =>
% 122.49/16.43                                           (((ap2apEq2) =>
% 122.49/16.43                                             (((beta1) =>
% 122.49/16.43                                               (((eta1) =>
% 122.49/16.43                                                 (((lam2lamEq) =>
% 122.49/16.43                                                   (((beta2) =>
% 122.49/16.43                                                     (((eta2) =>
% 122.49/16.43                                                       (((iffalseProp1) =>
% 122.49/16.43                                                         (((iffalseProp2) =>
% 122.49/16.43                                                           (((iftrueProp1) =>
% 122.49/16.43                                                             (((iftrueProp2) =>
% 122.49/16.43                                                               (((ifSingleton) =>
% 122.49/16.43                                                                 (((ifp) =>
% 122.49/16.43                                                                   (((theeq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrue) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iffalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrueorfalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1668])).
% 122.49/16.43  thf(zip_derived_cl1688, plain,
% 122.49/16.43      (~ (((lamProp) =>
% 122.49/16.43           (((lamp) =>
% 122.49/16.43             (((lam2p) =>
% 122.49/16.43               (((brelnall1) =>
% 122.49/16.43                 (((brelnall2) =>
% 122.49/16.43                   (((ex1E2) =>
% 122.49/16.43                     (((funcGraphProp1) =>
% 122.49/16.43                       (((funcGraphProp3) =>
% 122.49/16.43                         (((funcGraphProp2) =>
% 122.49/16.43                           (((funcextLem) =>
% 122.49/16.43                             (((funcGraphProp4) =>
% 122.49/16.43                               (((subbreln) =>
% 122.49/16.43                                 (((eqbreln) =>
% 122.49/16.43                                   (((funcext) =>
% 122.49/16.43                                     (((funcext2) =>
% 122.49/16.43                                       (((ap2apEq1) =>
% 122.49/16.43                                         (((ap2apEq2) =>
% 122.49/16.43                                           (((beta1) =>
% 122.49/16.43                                             (((eta1) =>
% 122.49/16.43                                               (((lam2lamEq) =>
% 122.49/16.43                                                 (((beta2) =>
% 122.49/16.43                                                   (((eta2) =>
% 122.49/16.43                                                     (((iffalseProp1) =>
% 122.49/16.43                                                       (((iffalseProp2) =>
% 122.49/16.43                                                         (((iftrueProp1) =>
% 122.49/16.43                                                           (((iftrueProp2) =>
% 122.49/16.43                                                             (((ifSingleton) =>
% 122.49/16.43                                                               (((ifp) =>
% 122.49/16.43                                                                 (((theeq) =>
% 122.49/16.43                                                                   (((iftrue) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iffalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrueorfalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1678])).
% 122.49/16.43  thf(zip_derived_cl1697, plain,
% 122.49/16.43      (~ (((lamp) =>
% 122.49/16.43           (((lam2p) =>
% 122.49/16.43             (((brelnall1) =>
% 122.49/16.43               (((brelnall2) =>
% 122.49/16.43                 (((ex1E2) =>
% 122.49/16.43                   (((funcGraphProp1) =>
% 122.49/16.43                     (((funcGraphProp3) =>
% 122.49/16.43                       (((funcGraphProp2) =>
% 122.49/16.43                         (((funcextLem) =>
% 122.49/16.43                           (((funcGraphProp4) =>
% 122.49/16.43                             (((subbreln) =>
% 122.49/16.43                               (((eqbreln) =>
% 122.49/16.43                                 (((funcext) =>
% 122.49/16.43                                   (((funcext2) =>
% 122.49/16.43                                     (((ap2apEq1) =>
% 122.49/16.43                                       (((ap2apEq2) =>
% 122.49/16.43                                         (((beta1) =>
% 122.49/16.43                                           (((eta1) =>
% 122.49/16.43                                             (((lam2lamEq) =>
% 122.49/16.43                                               (((beta2) =>
% 122.49/16.43                                                 (((eta2) =>
% 122.49/16.43                                                   (((iffalseProp1) =>
% 122.49/16.43                                                     (((iffalseProp2) =>
% 122.49/16.43                                                       (((iftrueProp1) =>
% 122.49/16.43                                                         (((iftrueProp2) =>
% 122.49/16.43                                                           (((ifSingleton) =>
% 122.49/16.43                                                             (((ifp) =>
% 122.49/16.43                                                               (((theeq) =>
% 122.49/16.43                                                                 (((iftrue) =>
% 122.49/16.43                                                                   (((iffalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (iftrueorfalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1688])).
% 122.49/16.43  thf(zip_derived_cl1706, plain,
% 122.49/16.43      (~ (((lam2p) =>
% 122.49/16.43           (((brelnall1) =>
% 122.49/16.43             (((brelnall2) =>
% 122.49/16.43               (((ex1E2) =>
% 122.49/16.43                 (((funcGraphProp1) =>
% 122.49/16.43                   (((funcGraphProp3) =>
% 122.49/16.43                     (((funcGraphProp2) =>
% 122.49/16.43                       (((funcextLem) =>
% 122.49/16.43                         (((funcGraphProp4) =>
% 122.49/16.43                           (((subbreln) =>
% 122.49/16.43                             (((eqbreln) =>
% 122.49/16.43                               (((funcext) =>
% 122.49/16.43                                 (((funcext2) =>
% 122.49/16.43                                   (((ap2apEq1) =>
% 122.49/16.43                                     (((ap2apEq2) =>
% 122.49/16.43                                       (((beta1) =>
% 122.49/16.43                                         (((eta1) =>
% 122.49/16.43                                           (((lam2lamEq) =>
% 122.49/16.43                                             (((beta2) =>
% 122.49/16.43                                               (((eta2) =>
% 122.49/16.43                                                 (((iffalseProp1) =>
% 122.49/16.43                                                   (((iffalseProp2) =>
% 122.49/16.43                                                     (((iftrueProp1) =>
% 122.49/16.43                                                       (((iftrueProp2) =>
% 122.49/16.43                                                         (((ifSingleton) =>
% 122.49/16.43                                                           (((ifp) =>
% 122.49/16.43                                                             (((theeq) =>
% 122.49/16.43                                                               (((iftrue) =>
% 122.49/16.43                                                                 (((iffalse) =>
% 122.49/16.43                                                                   (((iftrueorfalse) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1697])).
% 122.49/16.43  thf(zip_derived_cl1716, plain,
% 122.49/16.43      (~ (((brelnall1) =>
% 122.49/16.43           (((brelnall2) =>
% 122.49/16.43             (((ex1E2) =>
% 122.49/16.43               (((funcGraphProp1) =>
% 122.49/16.43                 (((funcGraphProp3) =>
% 122.49/16.43                   (((funcGraphProp2) =>
% 122.49/16.43                     (((funcextLem) =>
% 122.49/16.43                       (((funcGraphProp4) =>
% 122.49/16.43                         (((subbreln) =>
% 122.49/16.43                           (((eqbreln) =>
% 122.49/16.43                             (((funcext) =>
% 122.49/16.43                               (((funcext2) =>
% 122.49/16.43                                 (((ap2apEq1) =>
% 122.49/16.43                                   (((ap2apEq2) =>
% 122.49/16.43                                     (((beta1) =>
% 122.49/16.43                                       (((eta1) =>
% 122.49/16.43                                         (((lam2lamEq) =>
% 122.49/16.43                                           (((beta2) =>
% 122.49/16.43                                             (((eta2) =>
% 122.49/16.43                                               (((iffalseProp1) =>
% 122.49/16.43                                                 (((iffalseProp2) =>
% 122.49/16.43                                                   (((iftrueProp1) =>
% 122.49/16.43                                                     (((iftrueProp2) =>
% 122.49/16.43                                                       (((ifSingleton) =>
% 122.49/16.43                                                         (((ifp) =>
% 122.49/16.43                                                           (((theeq) =>
% 122.49/16.43                                                             (((iftrue) =>
% 122.49/16.43                                                               (((iffalse) =>
% 122.49/16.43                                                                 (((iftrueorfalse) =>
% 122.49/16.43                                                                   (((binintersectT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1706])).
% 122.49/16.43  thf(zip_derived_cl1725, plain,
% 122.49/16.43      (~ (((brelnall2) =>
% 122.49/16.43           (((ex1E2) =>
% 122.49/16.43             (((funcGraphProp1) =>
% 122.49/16.43               (((funcGraphProp3) =>
% 122.49/16.43                 (((funcGraphProp2) =>
% 122.49/16.43                   (((funcextLem) =>
% 122.49/16.43                     (((funcGraphProp4) =>
% 122.49/16.43                       (((subbreln) =>
% 122.49/16.43                         (((eqbreln) =>
% 122.49/16.43                           (((funcext) =>
% 122.49/16.43                             (((funcext2) =>
% 122.49/16.43                               (((ap2apEq1) =>
% 122.49/16.43                                 (((ap2apEq2) =>
% 122.49/16.43                                   (((beta1) =>
% 122.49/16.43                                     (((eta1) =>
% 122.49/16.43                                       (((lam2lamEq) =>
% 122.49/16.43                                         (((beta2) =>
% 122.49/16.43                                           (((eta2) =>
% 122.49/16.43                                             (((iffalseProp1) =>
% 122.49/16.43                                               (((iffalseProp2) =>
% 122.49/16.43                                                 (((iftrueProp1) =>
% 122.49/16.43                                                   (((iftrueProp2) =>
% 122.49/16.43                                                     (((ifSingleton) =>
% 122.49/16.43                                                       (((ifp) =>
% 122.49/16.43                                                         (((theeq) =>
% 122.49/16.43                                                           (((iftrue) =>
% 122.49/16.43                                                             (((iffalse) =>
% 122.49/16.43                                                               (((iftrueorfalse) =>
% 122.49/16.43                                                                 (((binintersectT_lem) =>
% 122.49/16.43                                                                   (((binunionT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1716])).
% 122.49/16.43  thf(zip_derived_cl1734, plain,
% 122.49/16.43      (~ (((ex1E2) =>
% 122.49/16.43           (((funcGraphProp1) =>
% 122.49/16.43             (((funcGraphProp3) =>
% 122.49/16.43               (((funcGraphProp2) =>
% 122.49/16.43                 (((funcextLem) =>
% 122.49/16.43                   (((funcGraphProp4) =>
% 122.49/16.43                     (((subbreln) =>
% 122.49/16.43                       (((eqbreln) =>
% 122.49/16.43                         (((funcext) =>
% 122.49/16.43                           (((funcext2) =>
% 122.49/16.43                             (((ap2apEq1) =>
% 122.49/16.43                               (((ap2apEq2) =>
% 122.49/16.43                                 (((beta1) =>
% 122.49/16.43                                   (((eta1) =>
% 122.49/16.43                                     (((lam2lamEq) =>
% 122.49/16.43                                       (((beta2) =>
% 122.49/16.43                                         (((eta2) =>
% 122.49/16.43                                           (((iffalseProp1) =>
% 122.49/16.43                                             (((iffalseProp2) =>
% 122.49/16.43                                               (((iftrueProp1) =>
% 122.49/16.43                                                 (((iftrueProp2) =>
% 122.49/16.43                                                   (((ifSingleton) =>
% 122.49/16.43                                                     (((ifp) =>
% 122.49/16.43                                                       (((theeq) =>
% 122.49/16.43                                                         (((iftrue) =>
% 122.49/16.43                                                           (((iffalse) =>
% 122.49/16.43                                                             (((iftrueorfalse) =>
% 122.49/16.43                                                               (((binintersectT_lem) =>
% 122.49/16.43                                                                 (((binunionT_lem) =>
% 122.49/16.43                                                                   (((powersetT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1725])).
% 122.49/16.43  thf(zip_derived_cl1742, plain,
% 122.49/16.43      (~ (((funcGraphProp1) =>
% 122.49/16.43           (((funcGraphProp3) =>
% 122.49/16.43             (((funcGraphProp2) =>
% 122.49/16.43               (((funcextLem) =>
% 122.49/16.43                 (((funcGraphProp4) =>
% 122.49/16.43                   (((subbreln) =>
% 122.49/16.43                     (((eqbreln) =>
% 122.49/16.43                       (((funcext) =>
% 122.49/16.43                         (((funcext2) =>
% 122.49/16.43                           (((ap2apEq1) =>
% 122.49/16.43                             (((ap2apEq2) =>
% 122.49/16.43                               (((beta1) =>
% 122.49/16.43                                 (((eta1) =>
% 122.49/16.43                                   (((lam2lamEq) =>
% 122.49/16.43                                     (((beta2) =>
% 122.49/16.43                                       (((eta2) =>
% 122.49/16.43                                         (((iffalseProp1) =>
% 122.49/16.43                                           (((iffalseProp2) =>
% 122.49/16.43                                             (((iftrueProp1) =>
% 122.49/16.43                                               (((iftrueProp2) =>
% 122.49/16.43                                                 (((ifSingleton) =>
% 122.49/16.43                                                   (((ifp) =>
% 122.49/16.43                                                     (((theeq) =>
% 122.49/16.43                                                       (((iftrue) =>
% 122.49/16.43                                                         (((iffalse) =>
% 122.49/16.43                                                           (((iftrueorfalse) =>
% 122.49/16.43                                                             (((binintersectT_lem) =>
% 122.49/16.43                                                               (((binunionT_lem) =>
% 122.49/16.43                                                                 (((powersetT_lem) =>
% 122.49/16.43                                                                   (((setminusT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1734])).
% 122.49/16.43  thf(zip_derived_cl1750, plain,
% 122.49/16.43      (~ (((funcGraphProp3) =>
% 122.49/16.43           (((funcGraphProp2) =>
% 122.49/16.43             (((funcextLem) =>
% 122.49/16.43               (((funcGraphProp4) =>
% 122.49/16.43                 (((subbreln) =>
% 122.49/16.43                   (((eqbreln) =>
% 122.49/16.43                     (((funcext) =>
% 122.49/16.43                       (((funcext2) =>
% 122.49/16.43                         (((ap2apEq1) =>
% 122.49/16.43                           (((ap2apEq2) =>
% 122.49/16.43                             (((beta1) =>
% 122.49/16.43                               (((eta1) =>
% 122.49/16.43                                 (((lam2lamEq) =>
% 122.49/16.43                                   (((beta2) =>
% 122.49/16.43                                     (((eta2) =>
% 122.49/16.43                                       (((iffalseProp1) =>
% 122.49/16.43                                         (((iffalseProp2) =>
% 122.49/16.43                                           (((iftrueProp1) =>
% 122.49/16.43                                             (((iftrueProp2) =>
% 122.49/16.43                                               (((ifSingleton) =>
% 122.49/16.43                                                 (((ifp) =>
% 122.49/16.43                                                   (((theeq) =>
% 122.49/16.43                                                     (((iftrue) =>
% 122.49/16.43                                                       (((iffalse) =>
% 122.49/16.43                                                         (((iftrueorfalse) =>
% 122.49/16.43                                                           (((binintersectT_lem) =>
% 122.49/16.43                                                             (((binunionT_lem) =>
% 122.49/16.43                                                               (((powersetT_lem) =>
% 122.49/16.43                                                                 (((setminusT_lem) =>
% 122.49/16.43                                                                   (((complementT_lem) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1742])).
% 122.49/16.43  thf(zip_derived_cl1761, plain,
% 122.49/16.43      (~ (((funcGraphProp2) =>
% 122.49/16.43           (((funcextLem) =>
% 122.49/16.43             (((funcGraphProp4) =>
% 122.49/16.43               (((subbreln) =>
% 122.49/16.43                 (((eqbreln) =>
% 122.49/16.43                   (((funcext) =>
% 122.49/16.43                     (((funcext2) =>
% 122.49/16.43                       (((ap2apEq1) =>
% 122.49/16.43                         (((ap2apEq2) =>
% 122.49/16.43                           (((beta1) =>
% 122.49/16.43                             (((eta1) =>
% 122.49/16.43                               (((lam2lamEq) =>
% 122.49/16.43                                 (((beta2) =>
% 122.49/16.43                                   (((eta2) =>
% 122.49/16.43                                     (((iffalseProp1) =>
% 122.49/16.43                                       (((iffalseProp2) =>
% 122.49/16.43                                         (((iftrueProp1) =>
% 122.49/16.43                                           (((iftrueProp2) =>
% 122.49/16.43                                             (((ifSingleton) =>
% 122.49/16.43                                               (((ifp) =>
% 122.49/16.43                                                 (((theeq) =>
% 122.49/16.43                                                   (((iftrue) =>
% 122.49/16.43                                                     (((iffalse) =>
% 122.49/16.43                                                       (((iftrueorfalse) =>
% 122.49/16.43                                                         (((binintersectT_lem) =>
% 122.49/16.43                                                           (((binunionT_lem) =>
% 122.49/16.43                                                             (((powersetT_lem) =>
% 122.49/16.43                                                               (((setminusT_lem) =>
% 122.49/16.43                                                                 (((complementT_lem) =>
% 122.49/16.43                                                                   (((setextT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1750])).
% 122.49/16.43  thf(zip_derived_cl1771, plain,
% 122.49/16.43      (~ (((funcextLem) =>
% 122.49/16.43           (((funcGraphProp4) =>
% 122.49/16.43             (((subbreln) =>
% 122.49/16.43               (((eqbreln) =>
% 122.49/16.43                 (((funcext) =>
% 122.49/16.43                   (((funcext2) =>
% 122.49/16.43                     (((ap2apEq1) =>
% 122.49/16.43                       (((ap2apEq2) =>
% 122.49/16.43                         (((beta1) =>
% 122.49/16.43                           (((eta1) =>
% 122.49/16.43                             (((lam2lamEq) =>
% 122.49/16.43                               (((beta2) =>
% 122.49/16.43                                 (((eta2) =>
% 122.49/16.43                                   (((iffalseProp1) =>
% 122.49/16.43                                     (((iffalseProp2) =>
% 122.49/16.43                                       (((iftrueProp1) =>
% 122.49/16.43                                         (((iftrueProp2) =>
% 122.49/16.43                                           (((ifSingleton) =>
% 122.49/16.43                                             (((ifp) =>
% 122.49/16.43                                               (((theeq) =>
% 122.49/16.43                                                 (((iftrue) =>
% 122.49/16.43                                                   (((iffalse) =>
% 122.49/16.43                                                     (((iftrueorfalse) =>
% 122.49/16.43                                                       (((binintersectT_lem) =>
% 122.49/16.43                                                         (((binunionT_lem) =>
% 122.49/16.43                                                           (((powersetT_lem) =>
% 122.49/16.43                                                             (((setminusT_lem) =>
% 122.49/16.43                                                               (((complementT_lem) =>
% 122.49/16.43                                                                 (((setextT) =>
% 122.49/16.43                                                                   (((subsetTI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1761])).
% 122.49/16.43  thf(zip_derived_cl1781, plain,
% 122.49/16.43      (~ (((funcGraphProp4) =>
% 122.49/16.43           (((subbreln) =>
% 122.49/16.43             (((eqbreln) =>
% 122.49/16.43               (((funcext) =>
% 122.49/16.43                 (((funcext2) =>
% 122.49/16.43                   (((ap2apEq1) =>
% 122.49/16.43                     (((ap2apEq2) =>
% 122.49/16.43                       (((beta1) =>
% 122.49/16.43                         (((eta1) =>
% 122.49/16.43                           (((lam2lamEq) =>
% 122.49/16.43                             (((beta2) =>
% 122.49/16.43                               (((eta2) =>
% 122.49/16.43                                 (((iffalseProp1) =>
% 122.49/16.43                                   (((iffalseProp2) =>
% 122.49/16.43                                     (((iftrueProp1) =>
% 122.49/16.43                                       (((iftrueProp2) =>
% 122.49/16.43                                         (((ifSingleton) =>
% 122.49/16.43                                           (((ifp) =>
% 122.49/16.43                                             (((theeq) =>
% 122.49/16.43                                               (((iftrue) =>
% 122.49/16.43                                                 (((iffalse) =>
% 122.49/16.43                                                   (((iftrueorfalse) =>
% 122.49/16.43                                                     (((binintersectT_lem) =>
% 122.49/16.43                                                       (((binunionT_lem) =>
% 122.49/16.43                                                         (((powersetT_lem) =>
% 122.49/16.43                                                           (((setminusT_lem) =>
% 122.49/16.43                                                             (((complementT_lem) =>
% 122.49/16.43                                                               (((setextT) =>
% 122.49/16.43                                                                 (((subsetTI) =>
% 122.49/16.43                                                                   (((powersetTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1771])).
% 122.49/16.43  thf(zip_derived_cl1790, plain,
% 122.49/16.43      (~ (((subbreln) =>
% 122.49/16.43           (((eqbreln) =>
% 122.49/16.43             (((funcext) =>
% 122.49/16.43               (((funcext2) =>
% 122.49/16.43                 (((ap2apEq1) =>
% 122.49/16.43                   (((ap2apEq2) =>
% 122.49/16.43                     (((beta1) =>
% 122.49/16.43                       (((eta1) =>
% 122.49/16.43                         (((lam2lamEq) =>
% 122.49/16.43                           (((beta2) =>
% 122.49/16.43                             (((eta2) =>
% 122.49/16.43                               (((iffalseProp1) =>
% 122.49/16.43                                 (((iffalseProp2) =>
% 122.49/16.43                                   (((iftrueProp1) =>
% 122.49/16.43                                     (((iftrueProp2) =>
% 122.49/16.43                                       (((ifSingleton) =>
% 122.49/16.43                                         (((ifp) =>
% 122.49/16.43                                           (((theeq) =>
% 122.49/16.43                                             (((iftrue) =>
% 122.49/16.43                                               (((iffalse) =>
% 122.49/16.43                                                 (((iftrueorfalse) =>
% 122.49/16.43                                                   (((binintersectT_lem) =>
% 122.49/16.43                                                     (((binunionT_lem) =>
% 122.49/16.43                                                       (((powersetT_lem) =>
% 122.49/16.43                                                         (((setminusT_lem) =>
% 122.49/16.43                                                           (((complementT_lem) =>
% 122.49/16.43                                                             (((setextT) =>
% 122.49/16.43                                                               (((subsetTI) =>
% 122.49/16.43                                                                 (((powersetTI1) =>
% 122.49/16.43                                                                   (((powersetTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1781])).
% 122.49/16.43  thf(zip_derived_cl1800, plain,
% 122.49/16.43      (~ (((eqbreln) =>
% 122.49/16.43           (((funcext) =>
% 122.49/16.43             (((funcext2) =>
% 122.49/16.43               (((ap2apEq1) =>
% 122.49/16.43                 (((ap2apEq2) =>
% 122.49/16.43                   (((beta1) =>
% 122.49/16.43                     (((eta1) =>
% 122.49/16.43                       (((lam2lamEq) =>
% 122.49/16.43                         (((beta2) =>
% 122.49/16.43                           (((eta2) =>
% 122.49/16.43                             (((iffalseProp1) =>
% 122.49/16.43                               (((iffalseProp2) =>
% 122.49/16.43                                 (((iftrueProp1) =>
% 122.49/16.43                                   (((iftrueProp2) =>
% 122.49/16.43                                     (((ifSingleton) =>
% 122.49/16.43                                       (((ifp) =>
% 122.49/16.43                                         (((theeq) =>
% 122.49/16.43                                           (((iftrue) =>
% 122.49/16.43                                             (((iffalse) =>
% 122.49/16.43                                               (((iftrueorfalse) =>
% 122.49/16.43                                                 (((binintersectT_lem) =>
% 122.49/16.43                                                   (((binunionT_lem) =>
% 122.49/16.43                                                     (((powersetT_lem) =>
% 122.49/16.43                                                       (((setminusT_lem) =>
% 122.49/16.43                                                         (((complementT_lem) =>
% 122.49/16.43                                                           (((setextT) =>
% 122.49/16.43                                                             (((subsetTI) =>
% 122.49/16.43                                                               (((powersetTI1) =>
% 122.49/16.43                                                                 (((powersetTE1) =>
% 122.49/16.43                                                                   (((complementTI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTELcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintersectTERcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contrasubsetT3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementI1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementE1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementSub2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (doubleComplementEq) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTnotintersectT) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementImpComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (contraSubsetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementTcontraSubset) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTILcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTIRcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binunionTEcontra) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2a) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2b) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (demorgan2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule0) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz13rule4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_3) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_4) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz1_5) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1SetBreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (choice2fnsingleton) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1all1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (subbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (eqbreln1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1invE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1compEex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionprop) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIL) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionIR) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionI) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionE) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionEcases) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (breln1unionCommutes) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2W) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2A) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (woz2B) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Ex1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1Equiv) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1E) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (image1I) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (injFuncSetFuncInj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (leftInvIsSurj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (surjCantorThm) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (foundation2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (notinself2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSp) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (omegaSclos) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peano0notS) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (peanoSinj) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (binintTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (transitivesetOp2) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (setunionTransitive) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (ordinalMinLem1) =>
% 122.49/16.43                                                                     ((
% 122.49/16.43                                                                     (!!) @ (
% 122.49/16.43                                                                     ^[Y0 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (ordinal @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y1 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (!!) @ (
% 122.49/16.43                                                                      ^[Y2 : $i]:
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y2 @ 
% 122.49/16.43                                                                      Y0) =>
% 122.49/16.43                                                                      ((
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ 
% 122.49/16.43                                                                      Y2) =>
% 122.49/16.43                                                                      (in @ 
% 122.49/16.43                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.43      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1790])).
% 122.49/16.43  thf(zip_derived_cl1812, plain,
% 122.49/16.43      (~ (((funcext) =>
% 122.49/16.43           (((funcext2) =>
% 122.49/16.43             (((ap2apEq1) =>
% 122.49/16.43               (((ap2apEq2) =>
% 122.49/16.43                 (((beta1) =>
% 122.49/16.43                   (((eta1) =>
% 122.49/16.43                     (((lam2lamEq) =>
% 122.49/16.43                       (((beta2) =>
% 122.49/16.43                         (((eta2) =>
% 122.49/16.43                           (((iffalseProp1) =>
% 122.49/16.43                             (((iffalseProp2) =>
% 122.49/16.43                               (((iftrueProp1) =>
% 122.49/16.43                                 (((iftrueProp2) =>
% 122.49/16.43                                   (((ifSingleton) =>
% 122.49/16.43                                     (((ifp) =>
% 122.49/16.43                                       (((theeq) =>
% 122.49/16.43                                         (((iftrue) =>
% 122.49/16.43                                           (((iffalse) =>
% 122.49/16.43                                             (((iftrueorfalse) =>
% 122.49/16.43                                               (((binintersectT_lem) =>
% 122.49/16.43                                                 (((binunionT_lem) =>
% 122.49/16.43                                                   (((powersetT_lem) =>
% 122.49/16.43                                                     (((setminusT_lem) =>
% 122.49/16.43                                                       (((complementT_lem) =>
% 122.49/16.43                                                         (((setextT) =>
% 122.49/16.43                                                           (((subsetTI) =>
% 122.49/16.43                                                             (((powersetTI1) =>
% 122.49/16.44                                                               (((powersetTE1) =>
% 122.49/16.44                                                                 (((complementTI1) =>
% 122.49/16.44                                                                   (((complementTE1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintersectTELcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintersectTERcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementI1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementE1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementEq) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1800])).
% 122.49/16.44  thf(zip_derived_cl1826, plain,
% 122.49/16.44      (~ (((funcext2) =>
% 122.49/16.44           (((ap2apEq1) =>
% 122.49/16.44             (((ap2apEq2) =>
% 122.49/16.44               (((beta1) =>
% 122.49/16.44                 (((eta1) =>
% 122.49/16.44                   (((lam2lamEq) =>
% 122.49/16.44                     (((beta2) =>
% 122.49/16.44                       (((eta2) =>
% 122.49/16.44                         (((iffalseProp1) =>
% 122.49/16.44                           (((iffalseProp2) =>
% 122.49/16.44                             (((iftrueProp1) =>
% 122.49/16.44                               (((iftrueProp2) =>
% 122.49/16.44                                 (((ifSingleton) =>
% 122.49/16.44                                   (((ifp) =>
% 122.49/16.44                                     (((theeq) =>
% 122.49/16.44                                       (((iftrue) =>
% 122.49/16.44                                         (((iffalse) =>
% 122.49/16.44                                           (((iftrueorfalse) =>
% 122.49/16.44                                             (((binintersectT_lem) =>
% 122.49/16.44                                               (((binunionT_lem) =>
% 122.49/16.44                                                 (((powersetT_lem) =>
% 122.49/16.44                                                   (((setminusT_lem) =>
% 122.49/16.44                                                     (((complementT_lem) =>
% 122.49/16.44                                                       (((setextT) =>
% 122.49/16.44                                                         (((subsetTI) =>
% 122.49/16.44                                                           (((powersetTI1) =>
% 122.49/16.44                                                             (((powersetTE1) =>
% 122.49/16.44                                                               (((complementTI1) =>
% 122.49/16.44                                                                 (((complementTE1) =>
% 122.49/16.44                                                                   (((binintersectTELcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintersectTERcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementI1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementE1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementEq) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1812])).
% 122.49/16.44  thf(zip_derived_cl1841, plain,
% 122.49/16.44      (~ (((ap2apEq1) =>
% 122.49/16.44           (((ap2apEq2) =>
% 122.49/16.44             (((beta1) =>
% 122.49/16.44               (((eta1) =>
% 122.49/16.44                 (((lam2lamEq) =>
% 122.49/16.44                   (((beta2) =>
% 122.49/16.44                     (((eta2) =>
% 122.49/16.44                       (((iffalseProp1) =>
% 122.49/16.44                         (((iffalseProp2) =>
% 122.49/16.44                           (((iftrueProp1) =>
% 122.49/16.44                             (((iftrueProp2) =>
% 122.49/16.44                               (((ifSingleton) =>
% 122.49/16.44                                 (((ifp) =>
% 122.49/16.44                                   (((theeq) =>
% 122.49/16.44                                     (((iftrue) =>
% 122.49/16.44                                       (((iffalse) =>
% 122.49/16.44                                         (((iftrueorfalse) =>
% 122.49/16.44                                           (((binintersectT_lem) =>
% 122.49/16.44                                             (((binunionT_lem) =>
% 122.49/16.44                                               (((powersetT_lem) =>
% 122.49/16.44                                                 (((setminusT_lem) =>
% 122.49/16.44                                                   (((complementT_lem) =>
% 122.49/16.44                                                     (((setextT) =>
% 122.49/16.44                                                       (((subsetTI) =>
% 122.49/16.44                                                         (((powersetTI1) =>
% 122.49/16.44                                                           (((powersetTE1) =>
% 122.49/16.44                                                             (((complementTI1) =>
% 122.49/16.44                                                               (((complementTE1) =>
% 122.49/16.44                                                                 (((binintersectTELcontra) =>
% 122.49/16.44                                                                   (((binintersectTERcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementI1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementE1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementEq) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1826])).
% 122.49/16.44  thf(zip_derived_cl1857, plain,
% 122.49/16.44      (~ (((ap2apEq2) =>
% 122.49/16.44           (((beta1) =>
% 122.49/16.44             (((eta1) =>
% 122.49/16.44               (((lam2lamEq) =>
% 122.49/16.44                 (((beta2) =>
% 122.49/16.44                   (((eta2) =>
% 122.49/16.44                     (((iffalseProp1) =>
% 122.49/16.44                       (((iffalseProp2) =>
% 122.49/16.44                         (((iftrueProp1) =>
% 122.49/16.44                           (((iftrueProp2) =>
% 122.49/16.44                             (((ifSingleton) =>
% 122.49/16.44                               (((ifp) =>
% 122.49/16.44                                 (((theeq) =>
% 122.49/16.44                                   (((iftrue) =>
% 122.49/16.44                                     (((iffalse) =>
% 122.49/16.44                                       (((iftrueorfalse) =>
% 122.49/16.44                                         (((binintersectT_lem) =>
% 122.49/16.44                                           (((binunionT_lem) =>
% 122.49/16.44                                             (((powersetT_lem) =>
% 122.49/16.44                                               (((setminusT_lem) =>
% 122.49/16.44                                                 (((complementT_lem) =>
% 122.49/16.44                                                   (((setextT) =>
% 122.49/16.44                                                     (((subsetTI) =>
% 122.49/16.44                                                       (((powersetTI1) =>
% 122.49/16.44                                                         (((powersetTE1) =>
% 122.49/16.44                                                           (((complementTI1) =>
% 122.49/16.44                                                             (((complementTE1) =>
% 122.49/16.44                                                               (((binintersectTELcontra) =>
% 122.49/16.44                                                                 (((binintersectTERcontra) =>
% 122.49/16.44                                                                   (((contrasubsetT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementI1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementE1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementEq) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1841])).
% 122.49/16.44  thf(zip_derived_cl1874, plain,
% 122.49/16.44      (~ (((beta1) =>
% 122.49/16.44           (((eta1) =>
% 122.49/16.44             (((lam2lamEq) =>
% 122.49/16.44               (((beta2) =>
% 122.49/16.44                 (((eta2) =>
% 122.49/16.44                   (((iffalseProp1) =>
% 122.49/16.44                     (((iffalseProp2) =>
% 122.49/16.44                       (((iftrueProp1) =>
% 122.49/16.44                         (((iftrueProp2) =>
% 122.49/16.44                           (((ifSingleton) =>
% 122.49/16.44                             (((ifp) =>
% 122.49/16.44                               (((theeq) =>
% 122.49/16.44                                 (((iftrue) =>
% 122.49/16.44                                   (((iffalse) =>
% 122.49/16.44                                     (((iftrueorfalse) =>
% 122.49/16.44                                       (((binintersectT_lem) =>
% 122.49/16.44                                         (((binunionT_lem) =>
% 122.49/16.44                                           (((powersetT_lem) =>
% 122.49/16.44                                             (((setminusT_lem) =>
% 122.49/16.44                                               (((complementT_lem) =>
% 122.49/16.44                                                 (((setextT) =>
% 122.49/16.44                                                   (((subsetTI) =>
% 122.49/16.44                                                     (((powersetTI1) =>
% 122.49/16.44                                                       (((powersetTE1) =>
% 122.49/16.44                                                         (((complementTI1) =>
% 122.49/16.44                                                           (((complementTE1) =>
% 122.49/16.44                                                             (((binintersectTELcontra) =>
% 122.49/16.44                                                               (((binintersectTERcontra) =>
% 122.49/16.44                                                                 (((contrasubsetT) =>
% 122.49/16.44                                                                   (((contrasubsetT1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementI1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementE1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementEq) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1857])).
% 122.49/16.44  thf(zip_derived_cl1890, plain,
% 122.49/16.44      (~ (((eta1) =>
% 122.49/16.44           (((lam2lamEq) =>
% 122.49/16.44             (((beta2) =>
% 122.49/16.44               (((eta2) =>
% 122.49/16.44                 (((iffalseProp1) =>
% 122.49/16.44                   (((iffalseProp2) =>
% 122.49/16.44                     (((iftrueProp1) =>
% 122.49/16.44                       (((iftrueProp2) =>
% 122.49/16.44                         (((ifSingleton) =>
% 122.49/16.44                           (((ifp) =>
% 122.49/16.44                             (((theeq) =>
% 122.49/16.44                               (((iftrue) =>
% 122.49/16.44                                 (((iffalse) =>
% 122.49/16.44                                   (((iftrueorfalse) =>
% 122.49/16.44                                     (((binintersectT_lem) =>
% 122.49/16.44                                       (((binunionT_lem) =>
% 122.49/16.44                                         (((powersetT_lem) =>
% 122.49/16.44                                           (((setminusT_lem) =>
% 122.49/16.44                                             (((complementT_lem) =>
% 122.49/16.44                                               (((setextT) =>
% 122.49/16.44                                                 (((subsetTI) =>
% 122.49/16.44                                                   (((powersetTI1) =>
% 122.49/16.44                                                     (((powersetTE1) =>
% 122.49/16.44                                                       (((complementTI1) =>
% 122.49/16.44                                                         (((complementTE1) =>
% 122.49/16.44                                                           (((binintersectTELcontra) =>
% 122.49/16.44                                                             (((binintersectTERcontra) =>
% 122.49/16.44                                                               (((contrasubsetT) =>
% 122.49/16.44                                                                 (((contrasubsetT1) =>
% 122.49/16.44                                                                   (((contrasubsetT2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contrasubsetT3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementI1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementE1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementEq) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1874])).
% 122.49/16.44  thf(zip_derived_cl1903, plain,
% 122.49/16.44      (~ (((lam2lamEq) =>
% 122.49/16.44           (((beta2) =>
% 122.49/16.44             (((eta2) =>
% 122.49/16.44               (((iffalseProp1) =>
% 122.49/16.44                 (((iffalseProp2) =>
% 122.49/16.44                   (((iftrueProp1) =>
% 122.49/16.44                     (((iftrueProp2) =>
% 122.49/16.44                       (((ifSingleton) =>
% 122.49/16.44                         (((ifp) =>
% 122.49/16.44                           (((theeq) =>
% 122.49/16.44                             (((iftrue) =>
% 122.49/16.44                               (((iffalse) =>
% 122.49/16.44                                 (((iftrueorfalse) =>
% 122.49/16.44                                   (((binintersectT_lem) =>
% 122.49/16.44                                     (((binunionT_lem) =>
% 122.49/16.44                                       (((powersetT_lem) =>
% 122.49/16.44                                         (((setminusT_lem) =>
% 122.49/16.44                                           (((complementT_lem) =>
% 122.49/16.44                                             (((setextT) =>
% 122.49/16.44                                               (((subsetTI) =>
% 122.49/16.44                                                 (((powersetTI1) =>
% 122.49/16.44                                                   (((powersetTE1) =>
% 122.49/16.44                                                     (((complementTI1) =>
% 122.49/16.44                                                       (((complementTE1) =>
% 122.49/16.44                                                         (((binintersectTELcontra) =>
% 122.49/16.44                                                           (((binintersectTERcontra) =>
% 122.49/16.44                                                             (((contrasubsetT) =>
% 122.49/16.44                                                               (((contrasubsetT1) =>
% 122.49/16.44                                                                 (((contrasubsetT2) =>
% 122.49/16.44                                                                   (((contrasubsetT3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementI1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementE1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementEq) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1890])).
% 122.49/16.44  thf(zip_derived_cl1916, plain,
% 122.49/16.44      (~ (((beta2) =>
% 122.49/16.44           (((eta2) =>
% 122.49/16.44             (((iffalseProp1) =>
% 122.49/16.44               (((iffalseProp2) =>
% 122.49/16.44                 (((iftrueProp1) =>
% 122.49/16.44                   (((iftrueProp2) =>
% 122.49/16.44                     (((ifSingleton) =>
% 122.49/16.44                       (((ifp) =>
% 122.49/16.44                         (((theeq) =>
% 122.49/16.44                           (((iftrue) =>
% 122.49/16.44                             (((iffalse) =>
% 122.49/16.44                               (((iftrueorfalse) =>
% 122.49/16.44                                 (((binintersectT_lem) =>
% 122.49/16.44                                   (((binunionT_lem) =>
% 122.49/16.44                                     (((powersetT_lem) =>
% 122.49/16.44                                       (((setminusT_lem) =>
% 122.49/16.44                                         (((complementT_lem) =>
% 122.49/16.44                                           (((setextT) =>
% 122.49/16.44                                             (((subsetTI) =>
% 122.49/16.44                                               (((powersetTI1) =>
% 122.49/16.44                                                 (((powersetTE1) =>
% 122.49/16.44                                                   (((complementTI1) =>
% 122.49/16.44                                                     (((complementTE1) =>
% 122.49/16.44                                                       (((binintersectTELcontra) =>
% 122.49/16.44                                                         (((binintersectTERcontra) =>
% 122.49/16.44                                                           (((contrasubsetT) =>
% 122.49/16.44                                                             (((contrasubsetT1) =>
% 122.49/16.44                                                               (((contrasubsetT2) =>
% 122.49/16.44                                                                 (((contrasubsetT3) =>
% 122.49/16.44                                                                   (((doubleComplementI1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementE1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementEq) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1903])).
% 122.49/16.44  thf(zip_derived_cl1930, plain,
% 122.49/16.44      (~ (((eta2) =>
% 122.49/16.44           (((iffalseProp1) =>
% 122.49/16.44             (((iffalseProp2) =>
% 122.49/16.44               (((iftrueProp1) =>
% 122.49/16.44                 (((iftrueProp2) =>
% 122.49/16.44                   (((ifSingleton) =>
% 122.49/16.44                     (((ifp) =>
% 122.49/16.44                       (((theeq) =>
% 122.49/16.44                         (((iftrue) =>
% 122.49/16.44                           (((iffalse) =>
% 122.49/16.44                             (((iftrueorfalse) =>
% 122.49/16.44                               (((binintersectT_lem) =>
% 122.49/16.44                                 (((binunionT_lem) =>
% 122.49/16.44                                   (((powersetT_lem) =>
% 122.49/16.44                                     (((setminusT_lem) =>
% 122.49/16.44                                       (((complementT_lem) =>
% 122.49/16.44                                         (((setextT) =>
% 122.49/16.44                                           (((subsetTI) =>
% 122.49/16.44                                             (((powersetTI1) =>
% 122.49/16.44                                               (((powersetTE1) =>
% 122.49/16.44                                                 (((complementTI1) =>
% 122.49/16.44                                                   (((complementTE1) =>
% 122.49/16.44                                                     (((binintersectTELcontra) =>
% 122.49/16.44                                                       (((binintersectTERcontra) =>
% 122.49/16.44                                                         (((contrasubsetT) =>
% 122.49/16.44                                                           (((contrasubsetT1) =>
% 122.49/16.44                                                             (((contrasubsetT2) =>
% 122.49/16.44                                                               (((contrasubsetT3) =>
% 122.49/16.44                                                                 (((doubleComplementI1) =>
% 122.49/16.44                                                                   (((doubleComplementE1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementEq) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1916])).
% 122.49/16.44  thf(zip_derived_cl1945, plain,
% 122.49/16.44      (~ (((iffalseProp1) =>
% 122.49/16.44           (((iffalseProp2) =>
% 122.49/16.44             (((iftrueProp1) =>
% 122.49/16.44               (((iftrueProp2) =>
% 122.49/16.44                 (((ifSingleton) =>
% 122.49/16.44                   (((ifp) =>
% 122.49/16.44                     (((theeq) =>
% 122.49/16.44                       (((iftrue) =>
% 122.49/16.44                         (((iffalse) =>
% 122.49/16.44                           (((iftrueorfalse) =>
% 122.49/16.44                             (((binintersectT_lem) =>
% 122.49/16.44                               (((binunionT_lem) =>
% 122.49/16.44                                 (((powersetT_lem) =>
% 122.49/16.44                                   (((setminusT_lem) =>
% 122.49/16.44                                     (((complementT_lem) =>
% 122.49/16.44                                       (((setextT) =>
% 122.49/16.44                                         (((subsetTI) =>
% 122.49/16.44                                           (((powersetTI1) =>
% 122.49/16.44                                             (((powersetTE1) =>
% 122.49/16.44                                               (((complementTI1) =>
% 122.49/16.44                                                 (((complementTE1) =>
% 122.49/16.44                                                   (((binintersectTELcontra) =>
% 122.49/16.44                                                     (((binintersectTERcontra) =>
% 122.49/16.44                                                       (((contrasubsetT) =>
% 122.49/16.44                                                         (((contrasubsetT1) =>
% 122.49/16.44                                                           (((contrasubsetT2) =>
% 122.49/16.44                                                             (((contrasubsetT3) =>
% 122.49/16.44                                                               (((doubleComplementI1) =>
% 122.49/16.44                                                                 (((doubleComplementE1) =>
% 122.49/16.44                                                                   (((doubleComplementSub1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementSub2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementEq) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1930])).
% 122.49/16.44  thf(zip_derived_cl1960, plain,
% 122.49/16.44      (~ (((iffalseProp2) =>
% 122.49/16.44           (((iftrueProp1) =>
% 122.49/16.44             (((iftrueProp2) =>
% 122.49/16.44               (((ifSingleton) =>
% 122.49/16.44                 (((ifp) =>
% 122.49/16.44                   (((theeq) =>
% 122.49/16.44                     (((iftrue) =>
% 122.49/16.44                       (((iffalse) =>
% 122.49/16.44                         (((iftrueorfalse) =>
% 122.49/16.44                           (((binintersectT_lem) =>
% 122.49/16.44                             (((binunionT_lem) =>
% 122.49/16.44                               (((powersetT_lem) =>
% 122.49/16.44                                 (((setminusT_lem) =>
% 122.49/16.44                                   (((complementT_lem) =>
% 122.49/16.44                                     (((setextT) =>
% 122.49/16.44                                       (((subsetTI) =>
% 122.49/16.44                                         (((powersetTI1) =>
% 122.49/16.44                                           (((powersetTE1) =>
% 122.49/16.44                                             (((complementTI1) =>
% 122.49/16.44                                               (((complementTE1) =>
% 122.49/16.44                                                 (((binintersectTELcontra) =>
% 122.49/16.44                                                   (((binintersectTERcontra) =>
% 122.49/16.44                                                     (((contrasubsetT) =>
% 122.49/16.44                                                       (((contrasubsetT1) =>
% 122.49/16.44                                                         (((contrasubsetT2) =>
% 122.49/16.44                                                           (((contrasubsetT3) =>
% 122.49/16.44                                                             (((doubleComplementI1) =>
% 122.49/16.44                                                               (((doubleComplementE1) =>
% 122.49/16.44                                                                 (((doubleComplementSub1) =>
% 122.49/16.44                                                                   (((doubleComplementSub2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (doubleComplementEq) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1945])).
% 122.49/16.44  thf(zip_derived_cl1982, plain,
% 122.49/16.44      (~ (((iftrueProp1) =>
% 122.49/16.44           (((iftrueProp2) =>
% 122.49/16.44             (((ifSingleton) =>
% 122.49/16.44               (((ifp) =>
% 122.49/16.44                 (((theeq) =>
% 122.49/16.44                   (((iftrue) =>
% 122.49/16.44                     (((iffalse) =>
% 122.49/16.44                       (((iftrueorfalse) =>
% 122.49/16.44                         (((binintersectT_lem) =>
% 122.49/16.44                           (((binunionT_lem) =>
% 122.49/16.44                             (((powersetT_lem) =>
% 122.49/16.44                               (((setminusT_lem) =>
% 122.49/16.44                                 (((complementT_lem) =>
% 122.49/16.44                                   (((setextT) =>
% 122.49/16.44                                     (((subsetTI) =>
% 122.49/16.44                                       (((powersetTI1) =>
% 122.49/16.44                                         (((powersetTE1) =>
% 122.49/16.44                                           (((complementTI1) =>
% 122.49/16.44                                             (((complementTE1) =>
% 122.49/16.44                                               (((binintersectTELcontra) =>
% 122.49/16.44                                                 (((binintersectTERcontra) =>
% 122.49/16.44                                                   (((contrasubsetT) =>
% 122.49/16.44                                                     (((contrasubsetT1) =>
% 122.49/16.44                                                       (((contrasubsetT2) =>
% 122.49/16.44                                                         (((contrasubsetT3) =>
% 122.49/16.44                                                           (((doubleComplementI1) =>
% 122.49/16.44                                                             (((doubleComplementE1) =>
% 122.49/16.44                                                               (((doubleComplementSub1) =>
% 122.49/16.44                                                                 (((doubleComplementSub2) =>
% 122.49/16.44                                                                   (((doubleComplementEq) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1960])).
% 122.49/16.44  thf(zip_derived_cl2001, plain,
% 122.49/16.44      (~ (((iftrueProp2) =>
% 122.49/16.44           (((ifSingleton) =>
% 122.49/16.44             (((ifp) =>
% 122.49/16.44               (((theeq) =>
% 122.49/16.44                 (((iftrue) =>
% 122.49/16.44                   (((iffalse) =>
% 122.49/16.44                     (((iftrueorfalse) =>
% 122.49/16.44                       (((binintersectT_lem) =>
% 122.49/16.44                         (((binunionT_lem) =>
% 122.49/16.44                           (((powersetT_lem) =>
% 122.49/16.44                             (((setminusT_lem) =>
% 122.49/16.44                               (((complementT_lem) =>
% 122.49/16.44                                 (((setextT) =>
% 122.49/16.44                                   (((subsetTI) =>
% 122.49/16.44                                     (((powersetTI1) =>
% 122.49/16.44                                       (((powersetTE1) =>
% 122.49/16.44                                         (((complementTI1) =>
% 122.49/16.44                                           (((complementTE1) =>
% 122.49/16.44                                             (((binintersectTELcontra) =>
% 122.49/16.44                                               (((binintersectTERcontra) =>
% 122.49/16.44                                                 (((contrasubsetT) =>
% 122.49/16.44                                                   (((contrasubsetT1) =>
% 122.49/16.44                                                     (((contrasubsetT2) =>
% 122.49/16.44                                                       (((contrasubsetT3) =>
% 122.49/16.44                                                         (((doubleComplementI1) =>
% 122.49/16.44                                                           (((doubleComplementE1) =>
% 122.49/16.44                                                             (((doubleComplementSub1) =>
% 122.49/16.44                                                               (((doubleComplementSub2) =>
% 122.49/16.44                                                                 (((doubleComplementEq) =>
% 122.49/16.44                                                                   (((complementTnotintersectT) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1982])).
% 122.49/16.44  thf(zip_derived_cl2017, plain,
% 122.49/16.44      (~ (((ifSingleton) =>
% 122.49/16.44           (((ifp) =>
% 122.49/16.44             (((theeq) =>
% 122.49/16.44               (((iftrue) =>
% 122.49/16.44                 (((iffalse) =>
% 122.49/16.44                   (((iftrueorfalse) =>
% 122.49/16.44                     (((binintersectT_lem) =>
% 122.49/16.44                       (((binunionT_lem) =>
% 122.49/16.44                         (((powersetT_lem) =>
% 122.49/16.44                           (((setminusT_lem) =>
% 122.49/16.44                             (((complementT_lem) =>
% 122.49/16.44                               (((setextT) =>
% 122.49/16.44                                 (((subsetTI) =>
% 122.49/16.44                                   (((powersetTI1) =>
% 122.49/16.44                                     (((powersetTE1) =>
% 122.49/16.44                                       (((complementTI1) =>
% 122.49/16.44                                         (((complementTE1) =>
% 122.49/16.44                                           (((binintersectTELcontra) =>
% 122.49/16.44                                             (((binintersectTERcontra) =>
% 122.49/16.44                                               (((contrasubsetT) =>
% 122.49/16.44                                                 (((contrasubsetT1) =>
% 122.49/16.44                                                   (((contrasubsetT2) =>
% 122.49/16.44                                                     (((contrasubsetT3) =>
% 122.49/16.44                                                       (((doubleComplementI1) =>
% 122.49/16.44                                                         (((doubleComplementE1) =>
% 122.49/16.44                                                           (((doubleComplementSub1) =>
% 122.49/16.44                                                             (((doubleComplementSub2) =>
% 122.49/16.44                                                               (((doubleComplementEq) =>
% 122.49/16.44                                                                 (((complementTnotintersectT) =>
% 122.49/16.44                                                                   (((complementImpComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2001])).
% 122.49/16.44  thf(zip_derived_cl2029, plain,
% 122.49/16.44      (~ (((ifp) =>
% 122.49/16.44           (((theeq) =>
% 122.49/16.44             (((iftrue) =>
% 122.49/16.44               (((iffalse) =>
% 122.49/16.44                 (((iftrueorfalse) =>
% 122.49/16.44                   (((binintersectT_lem) =>
% 122.49/16.44                     (((binunionT_lem) =>
% 122.49/16.44                       (((powersetT_lem) =>
% 122.49/16.44                         (((setminusT_lem) =>
% 122.49/16.44                           (((complementT_lem) =>
% 122.49/16.44                             (((setextT) =>
% 122.49/16.44                               (((subsetTI) =>
% 122.49/16.44                                 (((powersetTI1) =>
% 122.49/16.44                                   (((powersetTE1) =>
% 122.49/16.44                                     (((complementTI1) =>
% 122.49/16.44                                       (((complementTE1) =>
% 122.49/16.44                                         (((binintersectTELcontra) =>
% 122.49/16.44                                           (((binintersectTERcontra) =>
% 122.49/16.44                                             (((contrasubsetT) =>
% 122.49/16.44                                               (((contrasubsetT1) =>
% 122.49/16.44                                                 (((contrasubsetT2) =>
% 122.49/16.44                                                   (((contrasubsetT3) =>
% 122.49/16.44                                                     (((doubleComplementI1) =>
% 122.49/16.44                                                       (((doubleComplementE1) =>
% 122.49/16.44                                                         (((doubleComplementSub1) =>
% 122.49/16.44                                                           (((doubleComplementSub2) =>
% 122.49/16.44                                                             (((doubleComplementEq) =>
% 122.49/16.44                                                               (((complementTnotintersectT) =>
% 122.49/16.44                                                                 (((complementImpComplementIntersect) =>
% 122.49/16.44                                                                   (((complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2017])).
% 122.49/16.44  thf(zip_derived_cl2041, plain,
% 122.49/16.44      (~ (((theeq) =>
% 122.49/16.44           (((iftrue) =>
% 122.49/16.44             (((iffalse) =>
% 122.49/16.44               (((iftrueorfalse) =>
% 122.49/16.44                 (((binintersectT_lem) =>
% 122.49/16.44                   (((binunionT_lem) =>
% 122.49/16.44                     (((powersetT_lem) =>
% 122.49/16.44                       (((setminusT_lem) =>
% 122.49/16.44                         (((complementT_lem) =>
% 122.49/16.44                           (((setextT) =>
% 122.49/16.44                             (((subsetTI) =>
% 122.49/16.44                               (((powersetTI1) =>
% 122.49/16.44                                 (((powersetTE1) =>
% 122.49/16.44                                   (((complementTI1) =>
% 122.49/16.44                                     (((complementTE1) =>
% 122.49/16.44                                       (((binintersectTELcontra) =>
% 122.49/16.44                                         (((binintersectTERcontra) =>
% 122.49/16.44                                           (((contrasubsetT) =>
% 122.49/16.44                                             (((contrasubsetT1) =>
% 122.49/16.44                                               (((contrasubsetT2) =>
% 122.49/16.44                                                 (((contrasubsetT3) =>
% 122.49/16.44                                                   (((doubleComplementI1) =>
% 122.49/16.44                                                     (((doubleComplementE1) =>
% 122.49/16.44                                                       (((doubleComplementSub1) =>
% 122.49/16.44                                                         (((doubleComplementSub2) =>
% 122.49/16.44                                                           (((doubleComplementEq) =>
% 122.49/16.44                                                             (((complementTnotintersectT) =>
% 122.49/16.44                                                               (((complementImpComplementIntersect) =>
% 122.49/16.44                                                                 (((complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                   (((complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2029])).
% 122.49/16.44  thf(zip_derived_cl2053, plain,
% 122.49/16.44      (~ (((iftrue) =>
% 122.49/16.44           (((iffalse) =>
% 122.49/16.44             (((iftrueorfalse) =>
% 122.49/16.44               (((binintersectT_lem) =>
% 122.49/16.44                 (((binunionT_lem) =>
% 122.49/16.44                   (((powersetT_lem) =>
% 122.49/16.44                     (((setminusT_lem) =>
% 122.49/16.44                       (((complementT_lem) =>
% 122.49/16.44                         (((setextT) =>
% 122.49/16.44                           (((subsetTI) =>
% 122.49/16.44                             (((powersetTI1) =>
% 122.49/16.44                               (((powersetTE1) =>
% 122.49/16.44                                 (((complementTI1) =>
% 122.49/16.44                                   (((complementTE1) =>
% 122.49/16.44                                     (((binintersectTELcontra) =>
% 122.49/16.44                                       (((binintersectTERcontra) =>
% 122.49/16.44                                         (((contrasubsetT) =>
% 122.49/16.44                                           (((contrasubsetT1) =>
% 122.49/16.44                                             (((contrasubsetT2) =>
% 122.49/16.44                                               (((contrasubsetT3) =>
% 122.49/16.44                                                 (((doubleComplementI1) =>
% 122.49/16.44                                                   (((doubleComplementE1) =>
% 122.49/16.44                                                     (((doubleComplementSub1) =>
% 122.49/16.44                                                       (((doubleComplementSub2) =>
% 122.49/16.44                                                         (((doubleComplementEq) =>
% 122.49/16.44                                                           (((complementTnotintersectT) =>
% 122.49/16.44                                                             (((complementImpComplementIntersect) =>
% 122.49/16.44                                                               (((complementSubsetComplementIntersect) =>
% 122.49/16.44                                                                 (((complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                   (((contraSubsetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2041])).
% 122.49/16.44  thf(zip_derived_cl2062, plain,
% 122.49/16.44      (~ (((iffalse) =>
% 122.49/16.44           (((iftrueorfalse) =>
% 122.49/16.44             (((binintersectT_lem) =>
% 122.49/16.44               (((binunionT_lem) =>
% 122.49/16.44                 (((powersetT_lem) =>
% 122.49/16.44                   (((setminusT_lem) =>
% 122.49/16.44                     (((complementT_lem) =>
% 122.49/16.44                       (((setextT) =>
% 122.49/16.44                         (((subsetTI) =>
% 122.49/16.44                           (((powersetTI1) =>
% 122.49/16.44                             (((powersetTE1) =>
% 122.49/16.44                               (((complementTI1) =>
% 122.49/16.44                                 (((complementTE1) =>
% 122.49/16.44                                   (((binintersectTELcontra) =>
% 122.49/16.44                                     (((binintersectTERcontra) =>
% 122.49/16.44                                       (((contrasubsetT) =>
% 122.49/16.44                                         (((contrasubsetT1) =>
% 122.49/16.44                                           (((contrasubsetT2) =>
% 122.49/16.44                                             (((contrasubsetT3) =>
% 122.49/16.44                                               (((doubleComplementI1) =>
% 122.49/16.44                                                 (((doubleComplementE1) =>
% 122.49/16.44                                                   (((doubleComplementSub1) =>
% 122.49/16.44                                                     (((doubleComplementSub2) =>
% 122.49/16.44                                                       (((doubleComplementEq) =>
% 122.49/16.44                                                         (((complementTnotintersectT) =>
% 122.49/16.44                                                           (((complementImpComplementIntersect) =>
% 122.49/16.44                                                             (((complementSubsetComplementIntersect) =>
% 122.49/16.44                                                               (((complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                                 (((contraSubsetComplement) =>
% 122.49/16.44                                                                   (((complementTcontraSubset) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2053])).
% 122.49/16.44  thf(zip_derived_cl2072, plain,
% 122.49/16.44      (~ (((iftrueorfalse) =>
% 122.49/16.44           (((binintersectT_lem) =>
% 122.49/16.44             (((binunionT_lem) =>
% 122.49/16.44               (((powersetT_lem) =>
% 122.49/16.44                 (((setminusT_lem) =>
% 122.49/16.44                   (((complementT_lem) =>
% 122.49/16.44                     (((setextT) =>
% 122.49/16.44                       (((subsetTI) =>
% 122.49/16.44                         (((powersetTI1) =>
% 122.49/16.44                           (((powersetTE1) =>
% 122.49/16.44                             (((complementTI1) =>
% 122.49/16.44                               (((complementTE1) =>
% 122.49/16.44                                 (((binintersectTELcontra) =>
% 122.49/16.44                                   (((binintersectTERcontra) =>
% 122.49/16.44                                     (((contrasubsetT) =>
% 122.49/16.44                                       (((contrasubsetT1) =>
% 122.49/16.44                                         (((contrasubsetT2) =>
% 122.49/16.44                                           (((contrasubsetT3) =>
% 122.49/16.44                                             (((doubleComplementI1) =>
% 122.49/16.44                                               (((doubleComplementE1) =>
% 122.49/16.44                                                 (((doubleComplementSub1) =>
% 122.49/16.44                                                   (((doubleComplementSub2) =>
% 122.49/16.44                                                     (((doubleComplementEq) =>
% 122.49/16.44                                                       (((complementTnotintersectT) =>
% 122.49/16.44                                                         (((complementImpComplementIntersect) =>
% 122.49/16.44                                                           (((complementSubsetComplementIntersect) =>
% 122.49/16.44                                                             (((complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                               (((contraSubsetComplement) =>
% 122.49/16.44                                                                 (((complementTcontraSubset) =>
% 122.49/16.44                                                                   (((binunionTILcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2062])).
% 122.49/16.44  thf(zip_derived_cl2082, plain,
% 122.49/16.44      (~ (((binintersectT_lem) =>
% 122.49/16.44           (((binunionT_lem) =>
% 122.49/16.44             (((powersetT_lem) =>
% 122.49/16.44               (((setminusT_lem) =>
% 122.49/16.44                 (((complementT_lem) =>
% 122.49/16.44                   (((setextT) =>
% 122.49/16.44                     (((subsetTI) =>
% 122.49/16.44                       (((powersetTI1) =>
% 122.49/16.44                         (((powersetTE1) =>
% 122.49/16.44                           (((complementTI1) =>
% 122.49/16.44                             (((complementTE1) =>
% 122.49/16.44                               (((binintersectTELcontra) =>
% 122.49/16.44                                 (((binintersectTERcontra) =>
% 122.49/16.44                                   (((contrasubsetT) =>
% 122.49/16.44                                     (((contrasubsetT1) =>
% 122.49/16.44                                       (((contrasubsetT2) =>
% 122.49/16.44                                         (((contrasubsetT3) =>
% 122.49/16.44                                           (((doubleComplementI1) =>
% 122.49/16.44                                             (((doubleComplementE1) =>
% 122.49/16.44                                               (((doubleComplementSub1) =>
% 122.49/16.44                                                 (((doubleComplementSub2) =>
% 122.49/16.44                                                   (((doubleComplementEq) =>
% 122.49/16.44                                                     (((complementTnotintersectT) =>
% 122.49/16.44                                                       (((complementImpComplementIntersect) =>
% 122.49/16.44                                                         (((complementSubsetComplementIntersect) =>
% 122.49/16.44                                                           (((complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                             (((contraSubsetComplement) =>
% 122.49/16.44                                                               (((complementTcontraSubset) =>
% 122.49/16.44                                                                 (((binunionTILcontra) =>
% 122.49/16.44                                                                   (((binunionTIRcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2072])).
% 122.49/16.44  thf(zip_derived_cl2093, plain,
% 122.49/16.44      (~ (((binunionT_lem) =>
% 122.49/16.44           (((powersetT_lem) =>
% 122.49/16.44             (((setminusT_lem) =>
% 122.49/16.44               (((complementT_lem) =>
% 122.49/16.44                 (((setextT) =>
% 122.49/16.44                   (((subsetTI) =>
% 122.49/16.44                     (((powersetTI1) =>
% 122.49/16.44                       (((powersetTE1) =>
% 122.49/16.44                         (((complementTI1) =>
% 122.49/16.44                           (((complementTE1) =>
% 122.49/16.44                             (((binintersectTELcontra) =>
% 122.49/16.44                               (((binintersectTERcontra) =>
% 122.49/16.44                                 (((contrasubsetT) =>
% 122.49/16.44                                   (((contrasubsetT1) =>
% 122.49/16.44                                     (((contrasubsetT2) =>
% 122.49/16.44                                       (((contrasubsetT3) =>
% 122.49/16.44                                         (((doubleComplementI1) =>
% 122.49/16.44                                           (((doubleComplementE1) =>
% 122.49/16.44                                             (((doubleComplementSub1) =>
% 122.49/16.44                                               (((doubleComplementSub2) =>
% 122.49/16.44                                                 (((doubleComplementEq) =>
% 122.49/16.44                                                   (((complementTnotintersectT) =>
% 122.49/16.44                                                     (((complementImpComplementIntersect) =>
% 122.49/16.44                                                       (((complementSubsetComplementIntersect) =>
% 122.49/16.44                                                         (((complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                           (((contraSubsetComplement) =>
% 122.49/16.44                                                             (((complementTcontraSubset) =>
% 122.49/16.44                                                               (((binunionTILcontra) =>
% 122.49/16.44                                                                 (((binunionTIRcontra) =>
% 122.49/16.44                                                                   (((inIntersectImpInUnion) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule0) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz13rule4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_3) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_4) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz1_5) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1SetBreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (choice2fnsingleton) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setOfPairsIsBReln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1all1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (subbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (eqbreln1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1invE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1compEex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionprop) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIL) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionIR) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionI) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionEcases) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (breln1unionCommutes) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2W) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2A) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (woz2B) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Ex1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1Equiv) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1E) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (image1I) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncInInjFuncSet) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (injFuncSetFuncInj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncIn) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjFuncSetFuncSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (leftInvIsSurj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (surjCantorThm) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (foundation2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (notinself2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSp) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (omegaSclos) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peano0notS) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (peanoSinj) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binintTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (transitivesetOp2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (setunionTransitive) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (ordinalMinLem1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (!!) @ (
% 122.49/16.44                                                                     ^[Y0 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (ordinal @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y1 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (!!) @ (
% 122.49/16.44                                                                      ^[Y2 : $i]:
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y2 @ 
% 122.49/16.44                                                                      Y0) =>
% 122.49/16.44                                                                      ((
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ 
% 122.49/16.44                                                                      Y2) =>
% 122.49/16.44                                                                      (in @ 
% 122.49/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 122.49/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2082])).
% 122.49/16.44  thf(zip_derived_cl2103, plain,
% 122.49/16.44      (~ (((powersetT_lem) =>
% 122.49/16.44           (((setminusT_lem) =>
% 122.49/16.44             (((complementT_lem) =>
% 122.49/16.44               (((setextT) =>
% 122.49/16.44                 (((subsetTI) =>
% 122.49/16.44                   (((powersetTI1) =>
% 122.49/16.44                     (((powersetTE1) =>
% 122.49/16.44                       (((complementTI1) =>
% 122.49/16.44                         (((complementTE1) =>
% 122.49/16.44                           (((binintersectTELcontra) =>
% 122.49/16.44                             (((binintersectTERcontra) =>
% 122.49/16.44                               (((contrasubsetT) =>
% 122.49/16.44                                 (((contrasubsetT1) =>
% 122.49/16.44                                   (((contrasubsetT2) =>
% 122.49/16.44                                     (((contrasubsetT3) =>
% 122.49/16.44                                       (((doubleComplementI1) =>
% 122.49/16.44                                         (((doubleComplementE1) =>
% 122.49/16.44                                           (((doubleComplementSub1) =>
% 122.49/16.44                                             (((doubleComplementSub2) =>
% 122.49/16.44                                               (((doubleComplementEq) =>
% 122.49/16.44                                                 (((complementTnotintersectT) =>
% 122.49/16.44                                                   (((complementImpComplementIntersect) =>
% 122.49/16.44                                                     (((complementSubsetComplementIntersect) =>
% 122.49/16.44                                                       (((complementInPowersetComplementIntersect) =>
% 122.49/16.44                                                         (((contraSubsetComplement) =>
% 122.49/16.44                                                           (((complementTcontraSubset) =>
% 122.49/16.44                                                             (((binunionTILcontra) =>
% 122.49/16.44                                                               (((binunionTIRcontra) =>
% 122.49/16.44                                                                 (((inIntersectImpInUnion) =>
% 122.49/16.44                                                                   (((inIntersectImpInUnion2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inIntersectImpInIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTE) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (binunionTEcontra) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (complementUnionInPowersetComplement) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1b) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan1) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2a) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b2) =>
% 122.49/16.44                                                                     ((
% 122.49/16.44                                                                     (demorgan2b) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule0) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule3) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule4) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_3) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_4) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_5) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1all2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1SetBreln1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (choice2fnsingleton) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1all1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (subbreln1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (eqbreln1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1invprop) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1invI) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1invE) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1compprop) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1compI) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1compE) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1compEex) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionprop) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionIL) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionIR) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionI) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionE) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionEcases) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionCommutes) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz2Ex) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz2W) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz2A) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz2B) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (image1Ex) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (image1Ex1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (image1Equiv) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (image1E) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (image1I) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (injFuncSetFuncIn) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (injFuncSetFuncInj) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (leftInvIsSurj) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (surjCantorThm) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (foundation2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (notinself) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (notinself2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (omegaSp) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (omegaSclos) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (peano0notS) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (peanoSinj) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (transitivesetOp1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (binintTransitive) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (transitivesetOp2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (setunionTransitive) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (ordinalMinLem1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (!!) @ (
% 123.15/16.44                                                                     ^[Y0 : $i]:
% 123.15/16.44                                                                      ((
% 123.15/16.44                                                                      (ordinal @ 
% 123.15/16.44                                                                      Y0) =>
% 123.15/16.44                                                                      ((
% 123.15/16.44                                                                      (!!) @ (
% 123.15/16.44                                                                      ^[Y1 : $i]:
% 123.15/16.44                                                                      ((
% 123.15/16.44                                                                      (!!) @ (
% 123.15/16.44                                                                      ^[Y2 : $i]:
% 123.15/16.44                                                                      ((
% 123.15/16.44                                                                      (in @ 
% 123.15/16.44                                                                      Y2 @ 
% 123.15/16.44                                                                      Y0) =>
% 123.15/16.44                                                                      ((
% 123.15/16.44                                                                      (in @ 
% 123.15/16.44                                                                      Y1 @ 
% 123.15/16.44                                                                      Y2) =>
% 123.15/16.44                                                                      (in @ 
% 123.15/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2093])).
% 123.15/16.44  thf(zip_derived_cl2113, plain,
% 123.15/16.44      (~ (((setminusT_lem) =>
% 123.15/16.44           (((complementT_lem) =>
% 123.15/16.44             (((setextT) =>
% 123.15/16.44               (((subsetTI) =>
% 123.15/16.44                 (((powersetTI1) =>
% 123.15/16.44                   (((powersetTE1) =>
% 123.15/16.44                     (((complementTI1) =>
% 123.15/16.44                       (((complementTE1) =>
% 123.15/16.44                         (((binintersectTELcontra) =>
% 123.15/16.44                           (((binintersectTERcontra) =>
% 123.15/16.44                             (((contrasubsetT) =>
% 123.15/16.44                               (((contrasubsetT1) =>
% 123.15/16.44                                 (((contrasubsetT2) =>
% 123.15/16.44                                   (((contrasubsetT3) =>
% 123.15/16.44                                     (((doubleComplementI1) =>
% 123.15/16.44                                       (((doubleComplementE1) =>
% 123.15/16.44                                         (((doubleComplementSub1) =>
% 123.15/16.44                                           (((doubleComplementSub2) =>
% 123.15/16.44                                             (((doubleComplementEq) =>
% 123.15/16.44                                               (((complementTnotintersectT) =>
% 123.15/16.44                                                 (((complementImpComplementIntersect) =>
% 123.15/16.44                                                   (((complementSubsetComplementIntersect) =>
% 123.15/16.44                                                     (((complementInPowersetComplementIntersect) =>
% 123.15/16.44                                                       (((contraSubsetComplement) =>
% 123.15/16.44                                                         (((complementTcontraSubset) =>
% 123.15/16.44                                                           (((binunionTILcontra) =>
% 123.15/16.44                                                             (((binunionTIRcontra) =>
% 123.15/16.44                                                               (((inIntersectImpInUnion) =>
% 123.15/16.44                                                                 (((inIntersectImpInUnion2) =>
% 123.15/16.44                                                                   (((inIntersectImpInIntersectUnions) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (intersectInPowersetIntersectUnions) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (binunionTE) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (binunionTEcontra) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2a1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (complementUnionInPowersetComplement) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2a2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan1a) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan1b) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2a) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2b2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2b) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule0) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule3) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule4) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_3) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_4) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_5) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1all2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1SetBreln1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (choice2fnsingleton) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1all1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (subbreln1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (eqbreln1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1invprop) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1invI) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1invE) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1compprop) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1compI) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1compE) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1compEex) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionprop) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionIL) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionIR) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionI) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionE) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionEcases) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionCommutes) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz2Ex) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz2W) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz2A) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz2B) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (image1Ex) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (image1Ex1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (image1Equiv) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (image1E) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (image1I) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (injFuncSetFuncIn) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (injFuncSetFuncInj) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (leftInvIsSurj) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (surjCantorThm) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (foundation2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (notinself) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (notinself2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (omegaSp) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (omegaSclos) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (peano0notS) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (peanoSinj) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (transitivesetOp1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (binintTransitive) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (transitivesetOp2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (setunionTransitive) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (ordinalMinLem1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (!!) @ (
% 123.15/16.44                                                                     ^[Y0 : $i]:
% 123.15/16.44                                                                      ((
% 123.15/16.44                                                                      (ordinal @ 
% 123.15/16.44                                                                      Y0) =>
% 123.15/16.44                                                                      ((
% 123.15/16.44                                                                      (!!) @ (
% 123.15/16.44                                                                      ^[Y1 : $i]:
% 123.15/16.44                                                                      ((
% 123.15/16.44                                                                      (!!) @ (
% 123.15/16.44                                                                      ^[Y2 : $i]:
% 123.15/16.44                                                                      ((
% 123.15/16.44                                                                      (in @ 
% 123.15/16.44                                                                      Y2 @ 
% 123.15/16.44                                                                      Y0) =>
% 123.15/16.44                                                                      ((
% 123.15/16.44                                                                      (in @ 
% 123.15/16.44                                                                      Y1 @ 
% 123.15/16.44                                                                      Y2) =>
% 123.15/16.44                                                                      (in @ 
% 123.15/16.44                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.44      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2103])).
% 123.15/16.44  thf(zip_derived_cl2121, plain,
% 123.15/16.44      (~ (((complementT_lem) =>
% 123.15/16.44           (((setextT) =>
% 123.15/16.44             (((subsetTI) =>
% 123.15/16.44               (((powersetTI1) =>
% 123.15/16.44                 (((powersetTE1) =>
% 123.15/16.44                   (((complementTI1) =>
% 123.15/16.44                     (((complementTE1) =>
% 123.15/16.44                       (((binintersectTELcontra) =>
% 123.15/16.44                         (((binintersectTERcontra) =>
% 123.15/16.44                           (((contrasubsetT) =>
% 123.15/16.44                             (((contrasubsetT1) =>
% 123.15/16.44                               (((contrasubsetT2) =>
% 123.15/16.44                                 (((contrasubsetT3) =>
% 123.15/16.44                                   (((doubleComplementI1) =>
% 123.15/16.44                                     (((doubleComplementE1) =>
% 123.15/16.44                                       (((doubleComplementSub1) =>
% 123.15/16.44                                         (((doubleComplementSub2) =>
% 123.15/16.44                                           (((doubleComplementEq) =>
% 123.15/16.44                                             (((complementTnotintersectT) =>
% 123.15/16.44                                               (((complementImpComplementIntersect) =>
% 123.15/16.44                                                 (((complementSubsetComplementIntersect) =>
% 123.15/16.44                                                   (((complementInPowersetComplementIntersect) =>
% 123.15/16.44                                                     (((contraSubsetComplement) =>
% 123.15/16.44                                                       (((complementTcontraSubset) =>
% 123.15/16.44                                                         (((binunionTILcontra) =>
% 123.15/16.44                                                           (((binunionTIRcontra) =>
% 123.15/16.44                                                             (((inIntersectImpInUnion) =>
% 123.15/16.44                                                               (((inIntersectImpInUnion2) =>
% 123.15/16.44                                                                 (((inIntersectImpInIntersectUnions) =>
% 123.15/16.44                                                                   (((intersectInPowersetIntersectUnions) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (inComplementUnionImpNotIn1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (inComplementUnionImpInComplement1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (binunionTE) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (binunionTEcontra) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2a1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (complementUnionInPowersetComplement) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2a2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan1a) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan1b) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2a) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2b2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2b) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (demorgan2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule0) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule3) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz13rule4) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_3) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_4) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz1_5) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1all2) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1SetBreln1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (choice2fnsingleton) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1all1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (subbreln1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (eqbreln1) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1invprop) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1invI) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1invE) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1compprop) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1compI) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1compE) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1compEex) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionprop) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionIL) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionIR) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionI) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionE) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionEcases) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (breln1unionCommutes) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz2Ex) =>
% 123.15/16.44                                                                     ((
% 123.15/16.44                                                                     (woz2W) =>
% 123.15/16.44                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2113])).
% 123.15/16.45  thf(zip_derived_cl2130, plain,
% 123.15/16.45      (~ (((setextT) =>
% 123.15/16.45           (((subsetTI) =>
% 123.15/16.45             (((powersetTI1) =>
% 123.15/16.45               (((powersetTE1) =>
% 123.15/16.45                 (((complementTI1) =>
% 123.15/16.45                   (((complementTE1) =>
% 123.15/16.45                     (((binintersectTELcontra) =>
% 123.15/16.45                       (((binintersectTERcontra) =>
% 123.15/16.45                         (((contrasubsetT) =>
% 123.15/16.45                           (((contrasubsetT1) =>
% 123.15/16.45                             (((contrasubsetT2) =>
% 123.15/16.45                               (((contrasubsetT3) =>
% 123.15/16.45                                 (((doubleComplementI1) =>
% 123.15/16.45                                   (((doubleComplementE1) =>
% 123.15/16.45                                     (((doubleComplementSub1) =>
% 123.15/16.45                                       (((doubleComplementSub2) =>
% 123.15/16.45                                         (((doubleComplementEq) =>
% 123.15/16.45                                           (((complementTnotintersectT) =>
% 123.15/16.45                                             (((complementImpComplementIntersect) =>
% 123.15/16.45                                               (((complementSubsetComplementIntersect) =>
% 123.15/16.45                                                 (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                                                   (((contraSubsetComplement) =>
% 123.15/16.45                                                     (((complementTcontraSubset) =>
% 123.15/16.45                                                       (((binunionTILcontra) =>
% 123.15/16.45                                                         (((binunionTIRcontra) =>
% 123.15/16.45                                                           (((inIntersectImpInUnion) =>
% 123.15/16.45                                                             (((inIntersectImpInUnion2) =>
% 123.15/16.45                                                               (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                                                 (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                                                   (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (inComplementUnionImpInComplement1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binunionTE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binunionTEcontra) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (complementUnionInPowersetComplement) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2121])).
% 123.15/16.45  thf(zip_derived_cl2140, plain,
% 123.15/16.45      (~ (((subsetTI) =>
% 123.15/16.45           (((powersetTI1) =>
% 123.15/16.45             (((powersetTE1) =>
% 123.15/16.45               (((complementTI1) =>
% 123.15/16.45                 (((complementTE1) =>
% 123.15/16.45                   (((binintersectTELcontra) =>
% 123.15/16.45                     (((binintersectTERcontra) =>
% 123.15/16.45                       (((contrasubsetT) =>
% 123.15/16.45                         (((contrasubsetT1) =>
% 123.15/16.45                           (((contrasubsetT2) =>
% 123.15/16.45                             (((contrasubsetT3) =>
% 123.15/16.45                               (((doubleComplementI1) =>
% 123.15/16.45                                 (((doubleComplementE1) =>
% 123.15/16.45                                   (((doubleComplementSub1) =>
% 123.15/16.45                                     (((doubleComplementSub2) =>
% 123.15/16.45                                       (((doubleComplementEq) =>
% 123.15/16.45                                         (((complementTnotintersectT) =>
% 123.15/16.45                                           (((complementImpComplementIntersect) =>
% 123.15/16.45                                             (((complementSubsetComplementIntersect) =>
% 123.15/16.45                                               (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                                                 (((contraSubsetComplement) =>
% 123.15/16.45                                                   (((complementTcontraSubset) =>
% 123.15/16.45                                                     (((binunionTILcontra) =>
% 123.15/16.45                                                       (((binunionTIRcontra) =>
% 123.15/16.45                                                         (((inIntersectImpInUnion) =>
% 123.15/16.45                                                           (((inIntersectImpInUnion2) =>
% 123.15/16.45                                                             (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                                               (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                                                 (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                                                   (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binunionTE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binunionTEcontra) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (complementUnionInPowersetComplement) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2130])).
% 123.15/16.45  thf(zip_derived_cl2151, plain,
% 123.15/16.45      (~ (((powersetTI1) =>
% 123.15/16.45           (((powersetTE1) =>
% 123.15/16.45             (((complementTI1) =>
% 123.15/16.45               (((complementTE1) =>
% 123.15/16.45                 (((binintersectTELcontra) =>
% 123.15/16.45                   (((binintersectTERcontra) =>
% 123.15/16.45                     (((contrasubsetT) =>
% 123.15/16.45                       (((contrasubsetT1) =>
% 123.15/16.45                         (((contrasubsetT2) =>
% 123.15/16.45                           (((contrasubsetT3) =>
% 123.15/16.45                             (((doubleComplementI1) =>
% 123.15/16.45                               (((doubleComplementE1) =>
% 123.15/16.45                                 (((doubleComplementSub1) =>
% 123.15/16.45                                   (((doubleComplementSub2) =>
% 123.15/16.45                                     (((doubleComplementEq) =>
% 123.15/16.45                                       (((complementTnotintersectT) =>
% 123.15/16.45                                         (((complementImpComplementIntersect) =>
% 123.15/16.45                                           (((complementSubsetComplementIntersect) =>
% 123.15/16.45                                             (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                                               (((contraSubsetComplement) =>
% 123.15/16.45                                                 (((complementTcontraSubset) =>
% 123.15/16.45                                                   (((binunionTILcontra) =>
% 123.15/16.45                                                     (((binunionTIRcontra) =>
% 123.15/16.45                                                       (((inIntersectImpInUnion) =>
% 123.15/16.45                                                         (((inIntersectImpInUnion2) =>
% 123.15/16.45                                                           (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                                             (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                                               (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                                                 (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                                                   (((binunionTE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binunionTEcontra) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (complementUnionInPowersetComplement) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2140])).
% 123.15/16.45  thf(zip_derived_cl2159, plain,
% 123.15/16.45      (~ (((powersetTE1) =>
% 123.15/16.45           (((complementTI1) =>
% 123.15/16.45             (((complementTE1) =>
% 123.15/16.45               (((binintersectTELcontra) =>
% 123.15/16.45                 (((binintersectTERcontra) =>
% 123.15/16.45                   (((contrasubsetT) =>
% 123.15/16.45                     (((contrasubsetT1) =>
% 123.15/16.45                       (((contrasubsetT2) =>
% 123.15/16.45                         (((contrasubsetT3) =>
% 123.15/16.45                           (((doubleComplementI1) =>
% 123.15/16.45                             (((doubleComplementE1) =>
% 123.15/16.45                               (((doubleComplementSub1) =>
% 123.15/16.45                                 (((doubleComplementSub2) =>
% 123.15/16.45                                   (((doubleComplementEq) =>
% 123.15/16.45                                     (((complementTnotintersectT) =>
% 123.15/16.45                                       (((complementImpComplementIntersect) =>
% 123.15/16.45                                         (((complementSubsetComplementIntersect) =>
% 123.15/16.45                                           (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                                             (((contraSubsetComplement) =>
% 123.15/16.45                                               (((complementTcontraSubset) =>
% 123.15/16.45                                                 (((binunionTILcontra) =>
% 123.15/16.45                                                   (((binunionTIRcontra) =>
% 123.15/16.45                                                     (((inIntersectImpInUnion) =>
% 123.15/16.45                                                       (((inIntersectImpInUnion2) =>
% 123.15/16.45                                                         (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                                           (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                                             (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                                               (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                                                 (((binunionTE) =>
% 123.15/16.45                                                                   (((binunionTEcontra) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (complementUnionInPowersetComplement) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2151])).
% 123.15/16.45  thf(zip_derived_cl2166, plain,
% 123.15/16.45      (~ (((complementTI1) =>
% 123.15/16.45           (((complementTE1) =>
% 123.15/16.45             (((binintersectTELcontra) =>
% 123.15/16.45               (((binintersectTERcontra) =>
% 123.15/16.45                 (((contrasubsetT) =>
% 123.15/16.45                   (((contrasubsetT1) =>
% 123.15/16.45                     (((contrasubsetT2) =>
% 123.15/16.45                       (((contrasubsetT3) =>
% 123.15/16.45                         (((doubleComplementI1) =>
% 123.15/16.45                           (((doubleComplementE1) =>
% 123.15/16.45                             (((doubleComplementSub1) =>
% 123.15/16.45                               (((doubleComplementSub2) =>
% 123.15/16.45                                 (((doubleComplementEq) =>
% 123.15/16.45                                   (((complementTnotintersectT) =>
% 123.15/16.45                                     (((complementImpComplementIntersect) =>
% 123.15/16.45                                       (((complementSubsetComplementIntersect) =>
% 123.15/16.45                                         (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                                           (((contraSubsetComplement) =>
% 123.15/16.45                                             (((complementTcontraSubset) =>
% 123.15/16.45                                               (((binunionTILcontra) =>
% 123.15/16.45                                                 (((binunionTIRcontra) =>
% 123.15/16.45                                                   (((inIntersectImpInUnion) =>
% 123.15/16.45                                                     (((inIntersectImpInUnion2) =>
% 123.15/16.45                                                       (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                                         (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                                           (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                                             (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                                               (((binunionTE) =>
% 123.15/16.45                                                                 (((binunionTEcontra) =>
% 123.15/16.45                                                                   (((demorgan2a1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (complementUnionInPowersetComplement) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2159])).
% 123.15/16.45  thf(zip_derived_cl2173, plain,
% 123.15/16.45      (~ (((complementTE1) =>
% 123.15/16.45           (((binintersectTELcontra) =>
% 123.15/16.45             (((binintersectTERcontra) =>
% 123.15/16.45               (((contrasubsetT) =>
% 123.15/16.45                 (((contrasubsetT1) =>
% 123.15/16.45                   (((contrasubsetT2) =>
% 123.15/16.45                     (((contrasubsetT3) =>
% 123.15/16.45                       (((doubleComplementI1) =>
% 123.15/16.45                         (((doubleComplementE1) =>
% 123.15/16.45                           (((doubleComplementSub1) =>
% 123.15/16.45                             (((doubleComplementSub2) =>
% 123.15/16.45                               (((doubleComplementEq) =>
% 123.15/16.45                                 (((complementTnotintersectT) =>
% 123.15/16.45                                   (((complementImpComplementIntersect) =>
% 123.15/16.45                                     (((complementSubsetComplementIntersect) =>
% 123.15/16.45                                       (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                                         (((contraSubsetComplement) =>
% 123.15/16.45                                           (((complementTcontraSubset) =>
% 123.15/16.45                                             (((binunionTILcontra) =>
% 123.15/16.45                                               (((binunionTIRcontra) =>
% 123.15/16.45                                                 (((inIntersectImpInUnion) =>
% 123.15/16.45                                                   (((inIntersectImpInUnion2) =>
% 123.15/16.45                                                     (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                                       (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                                         (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                                           (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                                             (((binunionTE) =>
% 123.15/16.45                                                               (((binunionTEcontra) =>
% 123.15/16.45                                                                 (((demorgan2a1) =>
% 123.15/16.45                                                                   (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2166])).
% 123.15/16.45  thf(zip_derived_cl2180, plain,
% 123.15/16.45      (~ (((binintersectTELcontra) =>
% 123.15/16.45           (((binintersectTERcontra) =>
% 123.15/16.45             (((contrasubsetT) =>
% 123.15/16.45               (((contrasubsetT1) =>
% 123.15/16.45                 (((contrasubsetT2) =>
% 123.15/16.45                   (((contrasubsetT3) =>
% 123.15/16.45                     (((doubleComplementI1) =>
% 123.15/16.45                       (((doubleComplementE1) =>
% 123.15/16.45                         (((doubleComplementSub1) =>
% 123.15/16.45                           (((doubleComplementSub2) =>
% 123.15/16.45                             (((doubleComplementEq) =>
% 123.15/16.45                               (((complementTnotintersectT) =>
% 123.15/16.45                                 (((complementImpComplementIntersect) =>
% 123.15/16.45                                   (((complementSubsetComplementIntersect) =>
% 123.15/16.45                                     (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                                       (((contraSubsetComplement) =>
% 123.15/16.45                                         (((complementTcontraSubset) =>
% 123.15/16.45                                           (((binunionTILcontra) =>
% 123.15/16.45                                             (((binunionTIRcontra) =>
% 123.15/16.45                                               (((inIntersectImpInUnion) =>
% 123.15/16.45                                                 (((inIntersectImpInUnion2) =>
% 123.15/16.45                                                   (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                                     (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                                       (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                                         (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                                           (((binunionTE) =>
% 123.15/16.45                                                             (((binunionTEcontra) =>
% 123.15/16.45                                                               (((demorgan2a1) =>
% 123.15/16.45                                                                 (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                                                   (((demorgan2a2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2173])).
% 123.15/16.45  thf(zip_derived_cl2188, plain,
% 123.15/16.45      (~ (((binintersectTERcontra) =>
% 123.15/16.45           (((contrasubsetT) =>
% 123.15/16.45             (((contrasubsetT1) =>
% 123.15/16.45               (((contrasubsetT2) =>
% 123.15/16.45                 (((contrasubsetT3) =>
% 123.15/16.45                   (((doubleComplementI1) =>
% 123.15/16.45                     (((doubleComplementE1) =>
% 123.15/16.45                       (((doubleComplementSub1) =>
% 123.15/16.45                         (((doubleComplementSub2) =>
% 123.15/16.45                           (((doubleComplementEq) =>
% 123.15/16.45                             (((complementTnotintersectT) =>
% 123.15/16.45                               (((complementImpComplementIntersect) =>
% 123.15/16.45                                 (((complementSubsetComplementIntersect) =>
% 123.15/16.45                                   (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                                     (((contraSubsetComplement) =>
% 123.15/16.45                                       (((complementTcontraSubset) =>
% 123.15/16.45                                         (((binunionTILcontra) =>
% 123.15/16.45                                           (((binunionTIRcontra) =>
% 123.15/16.45                                             (((inIntersectImpInUnion) =>
% 123.15/16.45                                               (((inIntersectImpInUnion2) =>
% 123.15/16.45                                                 (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                                   (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                                     (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                                       (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                                         (((binunionTE) =>
% 123.15/16.45                                                           (((binunionTEcontra) =>
% 123.15/16.45                                                             (((demorgan2a1) =>
% 123.15/16.45                                                               (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                                                 (((demorgan2a2) =>
% 123.15/16.45                                                                   (((demorgan1a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2180])).
% 123.15/16.45  thf(zip_derived_cl2197, plain,
% 123.15/16.45      (~ (((contrasubsetT) =>
% 123.15/16.45           (((contrasubsetT1) =>
% 123.15/16.45             (((contrasubsetT2) =>
% 123.15/16.45               (((contrasubsetT3) =>
% 123.15/16.45                 (((doubleComplementI1) =>
% 123.15/16.45                   (((doubleComplementE1) =>
% 123.15/16.45                     (((doubleComplementSub1) =>
% 123.15/16.45                       (((doubleComplementSub2) =>
% 123.15/16.45                         (((doubleComplementEq) =>
% 123.15/16.45                           (((complementTnotintersectT) =>
% 123.15/16.45                             (((complementImpComplementIntersect) =>
% 123.15/16.45                               (((complementSubsetComplementIntersect) =>
% 123.15/16.45                                 (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                                   (((contraSubsetComplement) =>
% 123.15/16.45                                     (((complementTcontraSubset) =>
% 123.15/16.45                                       (((binunionTILcontra) =>
% 123.15/16.45                                         (((binunionTIRcontra) =>
% 123.15/16.45                                           (((inIntersectImpInUnion) =>
% 123.15/16.45                                             (((inIntersectImpInUnion2) =>
% 123.15/16.45                                               (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                                 (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                                   (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                                     (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                                       (((binunionTE) =>
% 123.15/16.45                                                         (((binunionTEcontra) =>
% 123.15/16.45                                                           (((demorgan2a1) =>
% 123.15/16.45                                                             (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                                               (((demorgan2a2) =>
% 123.15/16.45                                                                 (((demorgan1a) =>
% 123.15/16.45                                                                   (((demorgan1b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2188])).
% 123.15/16.45  thf(zip_derived_cl2207, plain,
% 123.15/16.45      (~ (((contrasubsetT1) =>
% 123.15/16.45           (((contrasubsetT2) =>
% 123.15/16.45             (((contrasubsetT3) =>
% 123.15/16.45               (((doubleComplementI1) =>
% 123.15/16.45                 (((doubleComplementE1) =>
% 123.15/16.45                   (((doubleComplementSub1) =>
% 123.15/16.45                     (((doubleComplementSub2) =>
% 123.15/16.45                       (((doubleComplementEq) =>
% 123.15/16.45                         (((complementTnotintersectT) =>
% 123.15/16.45                           (((complementImpComplementIntersect) =>
% 123.15/16.45                             (((complementSubsetComplementIntersect) =>
% 123.15/16.45                               (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                                 (((contraSubsetComplement) =>
% 123.15/16.45                                   (((complementTcontraSubset) =>
% 123.15/16.45                                     (((binunionTILcontra) =>
% 123.15/16.45                                       (((binunionTIRcontra) =>
% 123.15/16.45                                         (((inIntersectImpInUnion) =>
% 123.15/16.45                                           (((inIntersectImpInUnion2) =>
% 123.15/16.45                                             (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                               (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                                 (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                                   (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                                     (((binunionTE) =>
% 123.15/16.45                                                       (((binunionTEcontra) =>
% 123.15/16.45                                                         (((demorgan2a1) =>
% 123.15/16.45                                                           (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                                             (((demorgan2a2) =>
% 123.15/16.45                                                               (((demorgan1a) =>
% 123.15/16.45                                                                 (((demorgan1b) =>
% 123.15/16.45                                                                   (((demorgan1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2197])).
% 123.15/16.45  thf(zip_derived_cl2219, plain,
% 123.15/16.45      (~ (((contrasubsetT2) =>
% 123.15/16.45           (((contrasubsetT3) =>
% 123.15/16.45             (((doubleComplementI1) =>
% 123.15/16.45               (((doubleComplementE1) =>
% 123.15/16.45                 (((doubleComplementSub1) =>
% 123.15/16.45                   (((doubleComplementSub2) =>
% 123.15/16.45                     (((doubleComplementEq) =>
% 123.15/16.45                       (((complementTnotintersectT) =>
% 123.15/16.45                         (((complementImpComplementIntersect) =>
% 123.15/16.45                           (((complementSubsetComplementIntersect) =>
% 123.15/16.45                             (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                               (((contraSubsetComplement) =>
% 123.15/16.45                                 (((complementTcontraSubset) =>
% 123.15/16.45                                   (((binunionTILcontra) =>
% 123.15/16.45                                     (((binunionTIRcontra) =>
% 123.15/16.45                                       (((inIntersectImpInUnion) =>
% 123.15/16.45                                         (((inIntersectImpInUnion2) =>
% 123.15/16.45                                           (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                             (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                               (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                                 (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                                   (((binunionTE) =>
% 123.15/16.45                                                     (((binunionTEcontra) =>
% 123.15/16.45                                                       (((demorgan2a1) =>
% 123.15/16.45                                                         (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                                           (((demorgan2a2) =>
% 123.15/16.45                                                             (((demorgan1a) =>
% 123.15/16.45                                                               (((demorgan1b) =>
% 123.15/16.45                                                                 (((demorgan1) =>
% 123.15/16.45                                                                   (((demorgan2a) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2207])).
% 123.15/16.45  thf(zip_derived_cl2235, plain,
% 123.15/16.45      (~ (((contrasubsetT3) =>
% 123.15/16.45           (((doubleComplementI1) =>
% 123.15/16.45             (((doubleComplementE1) =>
% 123.15/16.45               (((doubleComplementSub1) =>
% 123.15/16.45                 (((doubleComplementSub2) =>
% 123.15/16.45                   (((doubleComplementEq) =>
% 123.15/16.45                     (((complementTnotintersectT) =>
% 123.15/16.45                       (((complementImpComplementIntersect) =>
% 123.15/16.45                         (((complementSubsetComplementIntersect) =>
% 123.15/16.45                           (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                             (((contraSubsetComplement) =>
% 123.15/16.45                               (((complementTcontraSubset) =>
% 123.15/16.45                                 (((binunionTILcontra) =>
% 123.15/16.45                                   (((binunionTIRcontra) =>
% 123.15/16.45                                     (((inIntersectImpInUnion) =>
% 123.15/16.45                                       (((inIntersectImpInUnion2) =>
% 123.15/16.45                                         (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                           (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                             (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                               (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                                 (((binunionTE) =>
% 123.15/16.45                                                   (((binunionTEcontra) =>
% 123.15/16.45                                                     (((demorgan2a1) =>
% 123.15/16.45                                                       (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                                         (((demorgan2a2) =>
% 123.15/16.45                                                           (((demorgan1a) =>
% 123.15/16.45                                                             (((demorgan1b) =>
% 123.15/16.45                                                               (((demorgan1) =>
% 123.15/16.45                                                                 (((demorgan2a) =>
% 123.15/16.45                                                                   (((demorgan2b2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2219])).
% 123.15/16.45  thf(zip_derived_cl2254, plain,
% 123.15/16.45      (~ (((doubleComplementI1) =>
% 123.15/16.45           (((doubleComplementE1) =>
% 123.15/16.45             (((doubleComplementSub1) =>
% 123.15/16.45               (((doubleComplementSub2) =>
% 123.15/16.45                 (((doubleComplementEq) =>
% 123.15/16.45                   (((complementTnotintersectT) =>
% 123.15/16.45                     (((complementImpComplementIntersect) =>
% 123.15/16.45                       (((complementSubsetComplementIntersect) =>
% 123.15/16.45                         (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                           (((contraSubsetComplement) =>
% 123.15/16.45                             (((complementTcontraSubset) =>
% 123.15/16.45                               (((binunionTILcontra) =>
% 123.15/16.45                                 (((binunionTIRcontra) =>
% 123.15/16.45                                   (((inIntersectImpInUnion) =>
% 123.15/16.45                                     (((inIntersectImpInUnion2) =>
% 123.15/16.45                                       (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                         (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                           (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                             (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                               (((binunionTE) =>
% 123.15/16.45                                                 (((binunionTEcontra) =>
% 123.15/16.45                                                   (((demorgan2a1) =>
% 123.15/16.45                                                     (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                                       (((demorgan2a2) =>
% 123.15/16.45                                                         (((demorgan1a) =>
% 123.15/16.45                                                           (((demorgan1b) =>
% 123.15/16.45                                                             (((demorgan1) =>
% 123.15/16.45                                                               (((demorgan2a) =>
% 123.15/16.45                                                                 (((demorgan2b2) =>
% 123.15/16.45                                                                   (((demorgan2b) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2235])).
% 123.15/16.45  thf(zip_derived_cl2267, plain,
% 123.15/16.45      (~ (((doubleComplementE1) =>
% 123.15/16.45           (((doubleComplementSub1) =>
% 123.15/16.45             (((doubleComplementSub2) =>
% 123.15/16.45               (((doubleComplementEq) =>
% 123.15/16.45                 (((complementTnotintersectT) =>
% 123.15/16.45                   (((complementImpComplementIntersect) =>
% 123.15/16.45                     (((complementSubsetComplementIntersect) =>
% 123.15/16.45                       (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                         (((contraSubsetComplement) =>
% 123.15/16.45                           (((complementTcontraSubset) =>
% 123.15/16.45                             (((binunionTILcontra) =>
% 123.15/16.45                               (((binunionTIRcontra) =>
% 123.15/16.45                                 (((inIntersectImpInUnion) =>
% 123.15/16.45                                   (((inIntersectImpInUnion2) =>
% 123.15/16.45                                     (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                       (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                         (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                           (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                             (((binunionTE) =>
% 123.15/16.45                                               (((binunionTEcontra) =>
% 123.15/16.45                                                 (((demorgan2a1) =>
% 123.15/16.45                                                   (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                                     (((demorgan2a2) =>
% 123.15/16.45                                                       (((demorgan1a) =>
% 123.15/16.45                                                         (((demorgan1b) =>
% 123.15/16.45                                                           (((demorgan1) =>
% 123.15/16.45                                                             (((demorgan2a) =>
% 123.15/16.45                                                               (((demorgan2b2) =>
% 123.15/16.45                                                                 (((demorgan2b) =>
% 123.15/16.45                                                                   (((demorgan2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2254])).
% 123.15/16.45  thf(zip_derived_cl2278, plain,
% 123.15/16.45      (~ (((doubleComplementSub1) =>
% 123.15/16.45           (((doubleComplementSub2) =>
% 123.15/16.45             (((doubleComplementEq) =>
% 123.15/16.45               (((complementTnotintersectT) =>
% 123.15/16.45                 (((complementImpComplementIntersect) =>
% 123.15/16.45                   (((complementSubsetComplementIntersect) =>
% 123.15/16.45                     (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                       (((contraSubsetComplement) =>
% 123.15/16.45                         (((complementTcontraSubset) =>
% 123.15/16.45                           (((binunionTILcontra) =>
% 123.15/16.45                             (((binunionTIRcontra) =>
% 123.15/16.45                               (((inIntersectImpInUnion) =>
% 123.15/16.45                                 (((inIntersectImpInUnion2) =>
% 123.15/16.45                                   (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                     (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                       (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                         (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                           (((binunionTE) =>
% 123.15/16.45                                             (((binunionTEcontra) =>
% 123.15/16.45                                               (((demorgan2a1) =>
% 123.15/16.45                                                 (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                                   (((demorgan2a2) =>
% 123.15/16.45                                                     (((demorgan1a) =>
% 123.15/16.45                                                       (((demorgan1b) =>
% 123.15/16.45                                                         (((demorgan1) =>
% 123.15/16.45                                                           (((demorgan2a) =>
% 123.15/16.45                                                             (((demorgan2b2) =>
% 123.15/16.45                                                               (((demorgan2b) =>
% 123.15/16.45                                                                 (((demorgan2) =>
% 123.15/16.45                                                                   (((woz13rule0) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2267])).
% 123.15/16.45  thf(zip_derived_cl2288, plain,
% 123.15/16.45      (~ (((doubleComplementSub2) =>
% 123.15/16.45           (((doubleComplementEq) =>
% 123.15/16.45             (((complementTnotintersectT) =>
% 123.15/16.45               (((complementImpComplementIntersect) =>
% 123.15/16.45                 (((complementSubsetComplementIntersect) =>
% 123.15/16.45                   (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                     (((contraSubsetComplement) =>
% 123.15/16.45                       (((complementTcontraSubset) =>
% 123.15/16.45                         (((binunionTILcontra) =>
% 123.15/16.45                           (((binunionTIRcontra) =>
% 123.15/16.45                             (((inIntersectImpInUnion) =>
% 123.15/16.45                               (((inIntersectImpInUnion2) =>
% 123.15/16.45                                 (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                   (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                     (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                       (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                         (((binunionTE) =>
% 123.15/16.45                                           (((binunionTEcontra) =>
% 123.15/16.45                                             (((demorgan2a1) =>
% 123.15/16.45                                               (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                                 (((demorgan2a2) =>
% 123.15/16.45                                                   (((demorgan1a) =>
% 123.15/16.45                                                     (((demorgan1b) =>
% 123.15/16.45                                                       (((demorgan1) =>
% 123.15/16.45                                                         (((demorgan2a) =>
% 123.15/16.45                                                           (((demorgan2b2) =>
% 123.15/16.45                                                             (((demorgan2b) =>
% 123.15/16.45                                                               (((demorgan2) =>
% 123.15/16.45                                                                 (((woz13rule0) =>
% 123.15/16.45                                                                   (((woz13rule1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2278])).
% 123.15/16.45  thf(zip_derived_cl2299, plain,
% 123.15/16.45      (~ (((doubleComplementEq) =>
% 123.15/16.45           (((complementTnotintersectT) =>
% 123.15/16.45             (((complementImpComplementIntersect) =>
% 123.15/16.45               (((complementSubsetComplementIntersect) =>
% 123.15/16.45                 (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                   (((contraSubsetComplement) =>
% 123.15/16.45                     (((complementTcontraSubset) =>
% 123.15/16.45                       (((binunionTILcontra) =>
% 123.15/16.45                         (((binunionTIRcontra) =>
% 123.15/16.45                           (((inIntersectImpInUnion) =>
% 123.15/16.45                             (((inIntersectImpInUnion2) =>
% 123.15/16.45                               (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                                 (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                   (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                     (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                       (((binunionTE) =>
% 123.15/16.45                                         (((binunionTEcontra) =>
% 123.15/16.45                                           (((demorgan2a1) =>
% 123.15/16.45                                             (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                               (((demorgan2a2) =>
% 123.15/16.45                                                 (((demorgan1a) =>
% 123.15/16.45                                                   (((demorgan1b) =>
% 123.15/16.45                                                     (((demorgan1) =>
% 123.15/16.45                                                       (((demorgan2a) =>
% 123.15/16.45                                                         (((demorgan2b2) =>
% 123.15/16.45                                                           (((demorgan2b) =>
% 123.15/16.45                                                             (((demorgan2) =>
% 123.15/16.45                                                               (((woz13rule0) =>
% 123.15/16.45                                                                 (((woz13rule1) =>
% 123.15/16.45                                                                   (((woz13rule2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2288])).
% 123.15/16.45  thf(zip_derived_cl2310, plain,
% 123.15/16.45      (~ (((complementTnotintersectT) =>
% 123.15/16.45           (((complementImpComplementIntersect) =>
% 123.15/16.45             (((complementSubsetComplementIntersect) =>
% 123.15/16.45               (((complementInPowersetComplementIntersect) =>
% 123.15/16.45                 (((contraSubsetComplement) =>
% 123.15/16.45                   (((complementTcontraSubset) =>
% 123.15/16.45                     (((binunionTILcontra) =>
% 123.15/16.45                       (((binunionTIRcontra) =>
% 123.15/16.45                         (((inIntersectImpInUnion) =>
% 123.15/16.45                           (((inIntersectImpInUnion2) =>
% 123.15/16.45                             (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                               (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                                 (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                   (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                     (((binunionTE) =>
% 123.15/16.45                                       (((binunionTEcontra) =>
% 123.15/16.45                                         (((demorgan2a1) =>
% 123.15/16.45                                           (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                             (((demorgan2a2) =>
% 123.15/16.45                                               (((demorgan1a) =>
% 123.15/16.45                                                 (((demorgan1b) =>
% 123.15/16.45                                                   (((demorgan1) =>
% 123.15/16.45                                                     (((demorgan2a) =>
% 123.15/16.45                                                       (((demorgan2b2) =>
% 123.15/16.45                                                         (((demorgan2b) =>
% 123.15/16.45                                                           (((demorgan2) =>
% 123.15/16.45                                                             (((woz13rule0) =>
% 123.15/16.45                                                               (((woz13rule1) =>
% 123.15/16.45                                                                 (((woz13rule2) =>
% 123.15/16.45                                                                   (((woz13rule3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2299])).
% 123.15/16.45  thf(zip_derived_cl2321, plain,
% 123.15/16.45      (~ (((complementImpComplementIntersect) =>
% 123.15/16.45           (((complementSubsetComplementIntersect) =>
% 123.15/16.45             (((complementInPowersetComplementIntersect) =>
% 123.15/16.45               (((contraSubsetComplement) =>
% 123.15/16.45                 (((complementTcontraSubset) =>
% 123.15/16.45                   (((binunionTILcontra) =>
% 123.15/16.45                     (((binunionTIRcontra) =>
% 123.15/16.45                       (((inIntersectImpInUnion) =>
% 123.15/16.45                         (((inIntersectImpInUnion2) =>
% 123.15/16.45                           (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                             (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                               (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                                 (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                   (((binunionTE) =>
% 123.15/16.45                                     (((binunionTEcontra) =>
% 123.15/16.45                                       (((demorgan2a1) =>
% 123.15/16.45                                         (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                           (((demorgan2a2) =>
% 123.15/16.45                                             (((demorgan1a) =>
% 123.15/16.45                                               (((demorgan1b) =>
% 123.15/16.45                                                 (((demorgan1) =>
% 123.15/16.45                                                   (((demorgan2a) =>
% 123.15/16.45                                                     (((demorgan2b2) =>
% 123.15/16.45                                                       (((demorgan2b) =>
% 123.15/16.45                                                         (((demorgan2) =>
% 123.15/16.45                                                           (((woz13rule0) =>
% 123.15/16.45                                                             (((woz13rule1) =>
% 123.15/16.45                                                               (((woz13rule2) =>
% 123.15/16.45                                                                 (((woz13rule3) =>
% 123.15/16.45                                                                   (((woz13rule4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2310])).
% 123.15/16.45  thf(zip_derived_cl2332, plain,
% 123.15/16.45      (~ (((complementSubsetComplementIntersect) =>
% 123.15/16.45           (((complementInPowersetComplementIntersect) =>
% 123.15/16.45             (((contraSubsetComplement) =>
% 123.15/16.45               (((complementTcontraSubset) =>
% 123.15/16.45                 (((binunionTILcontra) =>
% 123.15/16.45                   (((binunionTIRcontra) =>
% 123.15/16.45                     (((inIntersectImpInUnion) =>
% 123.15/16.45                       (((inIntersectImpInUnion2) =>
% 123.15/16.45                         (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                           (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                             (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                               (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                                 (((binunionTE) =>
% 123.15/16.45                                   (((binunionTEcontra) =>
% 123.15/16.45                                     (((demorgan2a1) =>
% 123.15/16.45                                       (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                         (((demorgan2a2) =>
% 123.15/16.45                                           (((demorgan1a) =>
% 123.15/16.45                                             (((demorgan1b) =>
% 123.15/16.45                                               (((demorgan1) =>
% 123.15/16.45                                                 (((demorgan2a) =>
% 123.15/16.45                                                   (((demorgan2b2) =>
% 123.15/16.45                                                     (((demorgan2b) =>
% 123.15/16.45                                                       (((demorgan2) =>
% 123.15/16.45                                                         (((woz13rule0) =>
% 123.15/16.45                                                           (((woz13rule1) =>
% 123.15/16.45                                                             (((woz13rule2) =>
% 123.15/16.45                                                               (((woz13rule3) =>
% 123.15/16.45                                                                 (((woz13rule4) =>
% 123.15/16.45                                                                   (((woz1_1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2321])).
% 123.15/16.45  thf(zip_derived_cl2341, plain,
% 123.15/16.45      (~ (((complementInPowersetComplementIntersect) =>
% 123.15/16.45           (((contraSubsetComplement) =>
% 123.15/16.45             (((complementTcontraSubset) =>
% 123.15/16.45               (((binunionTILcontra) =>
% 123.15/16.45                 (((binunionTIRcontra) =>
% 123.15/16.45                   (((inIntersectImpInUnion) =>
% 123.15/16.45                     (((inIntersectImpInUnion2) =>
% 123.15/16.45                       (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                         (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                           (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                             (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                               (((binunionTE) =>
% 123.15/16.45                                 (((binunionTEcontra) =>
% 123.15/16.45                                   (((demorgan2a1) =>
% 123.15/16.45                                     (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                       (((demorgan2a2) =>
% 123.15/16.45                                         (((demorgan1a) =>
% 123.15/16.45                                           (((demorgan1b) =>
% 123.15/16.45                                             (((demorgan1) =>
% 123.15/16.45                                               (((demorgan2a) =>
% 123.15/16.45                                                 (((demorgan2b2) =>
% 123.15/16.45                                                   (((demorgan2b) =>
% 123.15/16.45                                                     (((demorgan2) =>
% 123.15/16.45                                                       (((woz13rule0) =>
% 123.15/16.45                                                         (((woz13rule1) =>
% 123.15/16.45                                                           (((woz13rule2) =>
% 123.15/16.45                                                             (((woz13rule3) =>
% 123.15/16.45                                                               (((woz13rule4) =>
% 123.15/16.45                                                                 (((woz1_1) =>
% 123.15/16.45                                                                   (((woz1_2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2332])).
% 123.15/16.45  thf(zip_derived_cl2348, plain,
% 123.15/16.45      (~ (((contraSubsetComplement) =>
% 123.15/16.45           (((complementTcontraSubset) =>
% 123.15/16.45             (((binunionTILcontra) =>
% 123.15/16.45               (((binunionTIRcontra) =>
% 123.15/16.45                 (((inIntersectImpInUnion) =>
% 123.15/16.45                   (((inIntersectImpInUnion2) =>
% 123.15/16.45                     (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                       (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                         (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                           (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                             (((binunionTE) =>
% 123.15/16.45                               (((binunionTEcontra) =>
% 123.15/16.45                                 (((demorgan2a1) =>
% 123.15/16.45                                   (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                     (((demorgan2a2) =>
% 123.15/16.45                                       (((demorgan1a) =>
% 123.15/16.45                                         (((demorgan1b) =>
% 123.15/16.45                                           (((demorgan1) =>
% 123.15/16.45                                             (((demorgan2a) =>
% 123.15/16.45                                               (((demorgan2b2) =>
% 123.15/16.45                                                 (((demorgan2b) =>
% 123.15/16.45                                                   (((demorgan2) =>
% 123.15/16.45                                                     (((woz13rule0) =>
% 123.15/16.45                                                       (((woz13rule1) =>
% 123.15/16.45                                                         (((woz13rule2) =>
% 123.15/16.45                                                           (((woz13rule3) =>
% 123.15/16.45                                                             (((woz13rule4) =>
% 123.15/16.45                                                               (((woz1_1) =>
% 123.15/16.45                                                                 (((woz1_2) =>
% 123.15/16.45                                                                   (((woz1_3) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2341])).
% 123.15/16.45  thf(zip_derived_cl2355, plain,
% 123.15/16.45      (~ (((complementTcontraSubset) =>
% 123.15/16.45           (((binunionTILcontra) =>
% 123.15/16.45             (((binunionTIRcontra) =>
% 123.15/16.45               (((inIntersectImpInUnion) =>
% 123.15/16.45                 (((inIntersectImpInUnion2) =>
% 123.15/16.45                   (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                     (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                       (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                         (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                           (((binunionTE) =>
% 123.15/16.45                             (((binunionTEcontra) =>
% 123.15/16.45                               (((demorgan2a1) =>
% 123.15/16.45                                 (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                   (((demorgan2a2) =>
% 123.15/16.45                                     (((demorgan1a) =>
% 123.15/16.45                                       (((demorgan1b) =>
% 123.15/16.45                                         (((demorgan1) =>
% 123.15/16.45                                           (((demorgan2a) =>
% 123.15/16.45                                             (((demorgan2b2) =>
% 123.15/16.45                                               (((demorgan2b) =>
% 123.15/16.45                                                 (((demorgan2) =>
% 123.15/16.45                                                   (((woz13rule0) =>
% 123.15/16.45                                                     (((woz13rule1) =>
% 123.15/16.45                                                       (((woz13rule2) =>
% 123.15/16.45                                                         (((woz13rule3) =>
% 123.15/16.45                                                           (((woz13rule4) =>
% 123.15/16.45                                                             (((woz1_1) =>
% 123.15/16.45                                                               (((woz1_2) =>
% 123.15/16.45                                                                 (((woz1_3) =>
% 123.15/16.45                                                                   (((woz1_4) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2348])).
% 123.15/16.45  thf(zip_derived_cl2362, plain,
% 123.15/16.45      (~ (((binunionTILcontra) =>
% 123.15/16.45           (((binunionTIRcontra) =>
% 123.15/16.45             (((inIntersectImpInUnion) =>
% 123.15/16.45               (((inIntersectImpInUnion2) =>
% 123.15/16.45                 (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                   (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                     (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                       (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                         (((binunionTE) =>
% 123.15/16.45                           (((binunionTEcontra) =>
% 123.15/16.45                             (((demorgan2a1) =>
% 123.15/16.45                               (((complementUnionInPowersetComplement) =>
% 123.15/16.45                                 (((demorgan2a2) =>
% 123.15/16.45                                   (((demorgan1a) =>
% 123.15/16.45                                     (((demorgan1b) =>
% 123.15/16.45                                       (((demorgan1) =>
% 123.15/16.45                                         (((demorgan2a) =>
% 123.15/16.45                                           (((demorgan2b2) =>
% 123.15/16.45                                             (((demorgan2b) =>
% 123.15/16.45                                               (((demorgan2) =>
% 123.15/16.45                                                 (((woz13rule0) =>
% 123.15/16.45                                                   (((woz13rule1) =>
% 123.15/16.45                                                     (((woz13rule2) =>
% 123.15/16.45                                                       (((woz13rule3) =>
% 123.15/16.45                                                         (((woz13rule4) =>
% 123.15/16.45                                                           (((woz1_1) =>
% 123.15/16.45                                                             (((woz1_2) =>
% 123.15/16.45                                                               (((woz1_3) =>
% 123.15/16.45                                                                 (((woz1_4) =>
% 123.15/16.45                                                                   (((woz1_5) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2355])).
% 123.15/16.45  thf(zip_derived_cl2370, plain,
% 123.15/16.45      (~ (((binunionTIRcontra) =>
% 123.15/16.45           (((inIntersectImpInUnion) =>
% 123.15/16.45             (((inIntersectImpInUnion2) =>
% 123.15/16.45               (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45                 (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                   (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                     (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                       (((binunionTE) =>
% 123.15/16.45                         (((binunionTEcontra) =>
% 123.15/16.45                           (((demorgan2a1) =>
% 123.15/16.45                             (((complementUnionInPowersetComplement) =>
% 123.15/16.45                               (((demorgan2a2) =>
% 123.15/16.45                                 (((demorgan1a) =>
% 123.15/16.45                                   (((demorgan1b) =>
% 123.15/16.45                                     (((demorgan1) =>
% 123.15/16.45                                       (((demorgan2a) =>
% 123.15/16.45                                         (((demorgan2b2) =>
% 123.15/16.45                                           (((demorgan2b) =>
% 123.15/16.45                                             (((demorgan2) =>
% 123.15/16.45                                               (((woz13rule0) =>
% 123.15/16.45                                                 (((woz13rule1) =>
% 123.15/16.45                                                   (((woz13rule2) =>
% 123.15/16.45                                                     (((woz13rule3) =>
% 123.15/16.45                                                       (((woz13rule4) =>
% 123.15/16.45                                                         (((woz1_1) =>
% 123.15/16.45                                                           (((woz1_2) =>
% 123.15/16.45                                                             (((woz1_3) =>
% 123.15/16.45                                                               (((woz1_4) =>
% 123.15/16.45                                                                 (((woz1_5) =>
% 123.15/16.45                                                                   (((breln1all2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2362])).
% 123.15/16.45  thf(zip_derived_cl2379, plain,
% 123.15/16.45      (~ (((inIntersectImpInUnion) =>
% 123.15/16.45           (((inIntersectImpInUnion2) =>
% 123.15/16.45             (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45               (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45                 (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                   (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                     (((binunionTE) =>
% 123.15/16.45                       (((binunionTEcontra) =>
% 123.15/16.45                         (((demorgan2a1) =>
% 123.15/16.45                           (((complementUnionInPowersetComplement) =>
% 123.15/16.45                             (((demorgan2a2) =>
% 123.15/16.45                               (((demorgan1a) =>
% 123.15/16.45                                 (((demorgan1b) =>
% 123.15/16.45                                   (((demorgan1) =>
% 123.15/16.45                                     (((demorgan2a) =>
% 123.15/16.45                                       (((demorgan2b2) =>
% 123.15/16.45                                         (((demorgan2b) =>
% 123.15/16.45                                           (((demorgan2) =>
% 123.15/16.45                                             (((woz13rule0) =>
% 123.15/16.45                                               (((woz13rule1) =>
% 123.15/16.45                                                 (((woz13rule2) =>
% 123.15/16.45                                                   (((woz13rule3) =>
% 123.15/16.45                                                     (((woz13rule4) =>
% 123.15/16.45                                                       (((woz1_1) =>
% 123.15/16.45                                                         (((woz1_2) =>
% 123.15/16.45                                                           (((woz1_3) =>
% 123.15/16.45                                                             (((woz1_4) =>
% 123.15/16.45                                                               (((woz1_5) =>
% 123.15/16.45                                                                 (((breln1all2) =>
% 123.15/16.45                                                                   (((breln1SetBreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2370])).
% 123.15/16.45  thf(zip_derived_cl2389, plain,
% 123.15/16.45      (~ (((inIntersectImpInUnion2) =>
% 123.15/16.45           (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45             (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45               (((inComplementUnionImpNotIn1) =>
% 123.15/16.45                 (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                   (((binunionTE) =>
% 123.15/16.45                     (((binunionTEcontra) =>
% 123.15/16.45                       (((demorgan2a1) =>
% 123.15/16.45                         (((complementUnionInPowersetComplement) =>
% 123.15/16.45                           (((demorgan2a2) =>
% 123.15/16.45                             (((demorgan1a) =>
% 123.15/16.45                               (((demorgan1b) =>
% 123.15/16.45                                 (((demorgan1) =>
% 123.15/16.45                                   (((demorgan2a) =>
% 123.15/16.45                                     (((demorgan2b2) =>
% 123.15/16.45                                       (((demorgan2b) =>
% 123.15/16.45                                         (((demorgan2) =>
% 123.15/16.45                                           (((woz13rule0) =>
% 123.15/16.45                                             (((woz13rule1) =>
% 123.15/16.45                                               (((woz13rule2) =>
% 123.15/16.45                                                 (((woz13rule3) =>
% 123.15/16.45                                                   (((woz13rule4) =>
% 123.15/16.45                                                     (((woz1_1) =>
% 123.15/16.45                                                       (((woz1_2) =>
% 123.15/16.45                                                         (((woz1_3) =>
% 123.15/16.45                                                           (((woz1_4) =>
% 123.15/16.45                                                             (((woz1_5) =>
% 123.15/16.45                                                               (((breln1all2) =>
% 123.15/16.45                                                                 (((breln1SetBreln1) =>
% 123.15/16.45                                                                   (((choice2fnsingleton) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2379])).
% 123.15/16.45  thf(zip_derived_cl2399, plain,
% 123.15/16.45      (~ (((inIntersectImpInIntersectUnions) =>
% 123.15/16.45           (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45             (((inComplementUnionImpNotIn1) =>
% 123.15/16.45               (((inComplementUnionImpInComplement1) =>
% 123.15/16.45                 (((binunionTE) =>
% 123.15/16.45                   (((binunionTEcontra) =>
% 123.15/16.45                     (((demorgan2a1) =>
% 123.15/16.45                       (((complementUnionInPowersetComplement) =>
% 123.15/16.45                         (((demorgan2a2) =>
% 123.15/16.45                           (((demorgan1a) =>
% 123.15/16.45                             (((demorgan1b) =>
% 123.15/16.45                               (((demorgan1) =>
% 123.15/16.45                                 (((demorgan2a) =>
% 123.15/16.45                                   (((demorgan2b2) =>
% 123.15/16.45                                     (((demorgan2b) =>
% 123.15/16.45                                       (((demorgan2) =>
% 123.15/16.45                                         (((woz13rule0) =>
% 123.15/16.45                                           (((woz13rule1) =>
% 123.15/16.45                                             (((woz13rule2) =>
% 123.15/16.45                                               (((woz13rule3) =>
% 123.15/16.45                                                 (((woz13rule4) =>
% 123.15/16.45                                                   (((woz1_1) =>
% 123.15/16.45                                                     (((woz1_2) =>
% 123.15/16.45                                                       (((woz1_3) =>
% 123.15/16.45                                                         (((woz1_4) =>
% 123.15/16.45                                                           (((woz1_5) =>
% 123.15/16.45                                                             (((breln1all2) =>
% 123.15/16.45                                                               (((breln1SetBreln1) =>
% 123.15/16.45                                                                 (((choice2fnsingleton) =>
% 123.15/16.45                                                                   (((setOfPairsIsBReln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2389])).
% 123.15/16.45  thf(zip_derived_cl2408, plain,
% 123.15/16.45      (~ (((intersectInPowersetIntersectUnions) =>
% 123.15/16.45           (((inComplementUnionImpNotIn1) =>
% 123.15/16.45             (((inComplementUnionImpInComplement1) =>
% 123.15/16.45               (((binunionTE) =>
% 123.15/16.45                 (((binunionTEcontra) =>
% 123.15/16.45                   (((demorgan2a1) =>
% 123.15/16.45                     (((complementUnionInPowersetComplement) =>
% 123.15/16.45                       (((demorgan2a2) =>
% 123.15/16.45                         (((demorgan1a) =>
% 123.15/16.45                           (((demorgan1b) =>
% 123.15/16.45                             (((demorgan1) =>
% 123.15/16.45                               (((demorgan2a) =>
% 123.15/16.45                                 (((demorgan2b2) =>
% 123.15/16.45                                   (((demorgan2b) =>
% 123.15/16.45                                     (((demorgan2) =>
% 123.15/16.45                                       (((woz13rule0) =>
% 123.15/16.45                                         (((woz13rule1) =>
% 123.15/16.45                                           (((woz13rule2) =>
% 123.15/16.45                                             (((woz13rule3) =>
% 123.15/16.45                                               (((woz13rule4) =>
% 123.15/16.45                                                 (((woz1_1) =>
% 123.15/16.45                                                   (((woz1_2) =>
% 123.15/16.45                                                     (((woz1_3) =>
% 123.15/16.45                                                       (((woz1_4) =>
% 123.15/16.45                                                         (((woz1_5) =>
% 123.15/16.45                                                           (((breln1all2) =>
% 123.15/16.45                                                             (((breln1SetBreln1) =>
% 123.15/16.45                                                               (((choice2fnsingleton) =>
% 123.15/16.45                                                                 (((setOfPairsIsBReln1) =>
% 123.15/16.45                                                                   (((breln1all1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2399])).
% 123.15/16.45  thf(zip_derived_cl2417, plain,
% 123.15/16.45      (~ (((inComplementUnionImpNotIn1) =>
% 123.15/16.45           (((inComplementUnionImpInComplement1) =>
% 123.15/16.45             (((binunionTE) =>
% 123.15/16.45               (((binunionTEcontra) =>
% 123.15/16.45                 (((demorgan2a1) =>
% 123.15/16.45                   (((complementUnionInPowersetComplement) =>
% 123.15/16.45                     (((demorgan2a2) =>
% 123.15/16.45                       (((demorgan1a) =>
% 123.15/16.45                         (((demorgan1b) =>
% 123.15/16.45                           (((demorgan1) =>
% 123.15/16.45                             (((demorgan2a) =>
% 123.15/16.45                               (((demorgan2b2) =>
% 123.15/16.45                                 (((demorgan2b) =>
% 123.15/16.45                                   (((demorgan2) =>
% 123.15/16.45                                     (((woz13rule0) =>
% 123.15/16.45                                       (((woz13rule1) =>
% 123.15/16.45                                         (((woz13rule2) =>
% 123.15/16.45                                           (((woz13rule3) =>
% 123.15/16.45                                             (((woz13rule4) =>
% 123.15/16.45                                               (((woz1_1) =>
% 123.15/16.45                                                 (((woz1_2) =>
% 123.15/16.45                                                   (((woz1_3) =>
% 123.15/16.45                                                     (((woz1_4) =>
% 123.15/16.45                                                       (((woz1_5) =>
% 123.15/16.45                                                         (((breln1all2) =>
% 123.15/16.45                                                           (((breln1SetBreln1) =>
% 123.15/16.45                                                             (((choice2fnsingleton) =>
% 123.15/16.45                                                               (((setOfPairsIsBReln1) =>
% 123.15/16.45                                                                 (((breln1all1) =>
% 123.15/16.45                                                                   (((subbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2408])).
% 123.15/16.45  thf(zip_derived_cl2427, plain,
% 123.15/16.45      (~ (((inComplementUnionImpInComplement1) =>
% 123.15/16.45           (((binunionTE) =>
% 123.15/16.45             (((binunionTEcontra) =>
% 123.15/16.45               (((demorgan2a1) =>
% 123.15/16.45                 (((complementUnionInPowersetComplement) =>
% 123.15/16.45                   (((demorgan2a2) =>
% 123.15/16.45                     (((demorgan1a) =>
% 123.15/16.45                       (((demorgan1b) =>
% 123.15/16.45                         (((demorgan1) =>
% 123.15/16.45                           (((demorgan2a) =>
% 123.15/16.45                             (((demorgan2b2) =>
% 123.15/16.45                               (((demorgan2b) =>
% 123.15/16.45                                 (((demorgan2) =>
% 123.15/16.45                                   (((woz13rule0) =>
% 123.15/16.45                                     (((woz13rule1) =>
% 123.15/16.45                                       (((woz13rule2) =>
% 123.15/16.45                                         (((woz13rule3) =>
% 123.15/16.45                                           (((woz13rule4) =>
% 123.15/16.45                                             (((woz1_1) =>
% 123.15/16.45                                               (((woz1_2) =>
% 123.15/16.45                                                 (((woz1_3) =>
% 123.15/16.45                                                   (((woz1_4) =>
% 123.15/16.45                                                     (((woz1_5) =>
% 123.15/16.45                                                       (((breln1all2) =>
% 123.15/16.45                                                         (((breln1SetBreln1) =>
% 123.15/16.45                                                           (((choice2fnsingleton) =>
% 123.15/16.45                                                             (((setOfPairsIsBReln1) =>
% 123.15/16.45                                                               (((breln1all1) =>
% 123.15/16.45                                                                 (((subbreln1) =>
% 123.15/16.45                                                                   (((eqbreln1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1invE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1compEex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionprop) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIL) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionIR) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionI) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionE) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionEcases) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (breln1unionCommutes) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2W) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2A) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (woz2B) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Ex1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1Equiv) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1E) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (image1I) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (injFuncSetFuncInj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (leftInvIsSurj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (surjCantorThm) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (foundation2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (notinself2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSp) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (omegaSclos) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peano0notS) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (peanoSinj) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (binintTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (transitivesetOp2) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (setunionTransitive) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (ordinalMinLem1) =>
% 123.15/16.45                                                                     ((
% 123.15/16.45                                                                     (!!) @ (
% 123.15/16.45                                                                     ^[Y0 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (ordinal @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y1 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (!!) @ (
% 123.15/16.45                                                                      ^[Y2 : $i]:
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y2 @ 
% 123.15/16.45                                                                      Y0) =>
% 123.15/16.45                                                                      ((
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ 
% 123.15/16.45                                                                      Y2) =>
% 123.15/16.45                                                                      (in @ 
% 123.15/16.45                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.45      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2417])).
% 123.15/16.45  thf(zip_derived_cl2437, plain,
% 123.15/16.45      (~ (((binunionTE) =>
% 123.15/16.45           (((binunionTEcontra) =>
% 123.15/16.45             (((demorgan2a1) =>
% 123.15/16.45               (((complementUnionInPowersetComplement) =>
% 123.15/16.45                 (((demorgan2a2) =>
% 123.15/16.46                   (((demorgan1a) =>
% 123.15/16.46                     (((demorgan1b) =>
% 123.15/16.46                       (((demorgan1) =>
% 123.15/16.46                         (((demorgan2a) =>
% 123.15/16.46                           (((demorgan2b2) =>
% 123.15/16.46                             (((demorgan2b) =>
% 123.15/16.46                               (((demorgan2) =>
% 123.15/16.46                                 (((woz13rule0) =>
% 123.15/16.46                                   (((woz13rule1) =>
% 123.15/16.46                                     (((woz13rule2) =>
% 123.15/16.46                                       (((woz13rule3) =>
% 123.15/16.46                                         (((woz13rule4) =>
% 123.15/16.46                                           (((woz1_1) =>
% 123.15/16.46                                             (((woz1_2) =>
% 123.15/16.46                                               (((woz1_3) =>
% 123.15/16.46                                                 (((woz1_4) =>
% 123.15/16.46                                                   (((woz1_5) =>
% 123.15/16.46                                                     (((breln1all2) =>
% 123.15/16.46                                                       (((breln1SetBreln1) =>
% 123.15/16.46                                                         (((choice2fnsingleton) =>
% 123.15/16.46                                                           (((setOfPairsIsBReln1) =>
% 123.15/16.46                                                             (((breln1all1) =>
% 123.15/16.46                                                               (((subbreln1) =>
% 123.15/16.46                                                                 (((eqbreln1) =>
% 123.15/16.46                                                                   (((breln1invprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1invI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1invE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compEex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIL) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIR) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2427])).
% 123.15/16.46  thf(zip_derived_cl2448, plain,
% 123.15/16.46      (~ (((binunionTEcontra) =>
% 123.15/16.46           (((demorgan2a1) =>
% 123.15/16.46             (((complementUnionInPowersetComplement) =>
% 123.15/16.46               (((demorgan2a2) =>
% 123.15/16.46                 (((demorgan1a) =>
% 123.15/16.46                   (((demorgan1b) =>
% 123.15/16.46                     (((demorgan1) =>
% 123.15/16.46                       (((demorgan2a) =>
% 123.15/16.46                         (((demorgan2b2) =>
% 123.15/16.46                           (((demorgan2b) =>
% 123.15/16.46                             (((demorgan2) =>
% 123.15/16.46                               (((woz13rule0) =>
% 123.15/16.46                                 (((woz13rule1) =>
% 123.15/16.46                                   (((woz13rule2) =>
% 123.15/16.46                                     (((woz13rule3) =>
% 123.15/16.46                                       (((woz13rule4) =>
% 123.15/16.46                                         (((woz1_1) =>
% 123.15/16.46                                           (((woz1_2) =>
% 123.15/16.46                                             (((woz1_3) =>
% 123.15/16.46                                               (((woz1_4) =>
% 123.15/16.46                                                 (((woz1_5) =>
% 123.15/16.46                                                   (((breln1all2) =>
% 123.15/16.46                                                     (((breln1SetBreln1) =>
% 123.15/16.46                                                       (((choice2fnsingleton) =>
% 123.15/16.46                                                         (((setOfPairsIsBReln1) =>
% 123.15/16.46                                                           (((breln1all1) =>
% 123.15/16.46                                                             (((subbreln1) =>
% 123.15/16.46                                                               (((eqbreln1) =>
% 123.15/16.46                                                                 (((breln1invprop) =>
% 123.15/16.46                                                                   (((breln1invI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1invE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compEex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIL) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIR) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2437])).
% 123.15/16.46  thf(zip_derived_cl2459, plain,
% 123.15/16.46      (~ (((demorgan2a1) =>
% 123.15/16.46           (((complementUnionInPowersetComplement) =>
% 123.15/16.46             (((demorgan2a2) =>
% 123.15/16.46               (((demorgan1a) =>
% 123.15/16.46                 (((demorgan1b) =>
% 123.15/16.46                   (((demorgan1) =>
% 123.15/16.46                     (((demorgan2a) =>
% 123.15/16.46                       (((demorgan2b2) =>
% 123.15/16.46                         (((demorgan2b) =>
% 123.15/16.46                           (((demorgan2) =>
% 123.15/16.46                             (((woz13rule0) =>
% 123.15/16.46                               (((woz13rule1) =>
% 123.15/16.46                                 (((woz13rule2) =>
% 123.15/16.46                                   (((woz13rule3) =>
% 123.15/16.46                                     (((woz13rule4) =>
% 123.15/16.46                                       (((woz1_1) =>
% 123.15/16.46                                         (((woz1_2) =>
% 123.15/16.46                                           (((woz1_3) =>
% 123.15/16.46                                             (((woz1_4) =>
% 123.15/16.46                                               (((woz1_5) =>
% 123.15/16.46                                                 (((breln1all2) =>
% 123.15/16.46                                                   (((breln1SetBreln1) =>
% 123.15/16.46                                                     (((choice2fnsingleton) =>
% 123.15/16.46                                                       (((setOfPairsIsBReln1) =>
% 123.15/16.46                                                         (((breln1all1) =>
% 123.15/16.46                                                           (((subbreln1) =>
% 123.15/16.46                                                             (((eqbreln1) =>
% 123.15/16.46                                                               (((breln1invprop) =>
% 123.15/16.46                                                                 (((breln1invI) =>
% 123.15/16.46                                                                   (((breln1invE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compEex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIL) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIR) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2448])).
% 123.15/16.46  thf(zip_derived_cl2470, plain,
% 123.15/16.46      (~ (((complementUnionInPowersetComplement) =>
% 123.15/16.46           (((demorgan2a2) =>
% 123.15/16.46             (((demorgan1a) =>
% 123.15/16.46               (((demorgan1b) =>
% 123.15/16.46                 (((demorgan1) =>
% 123.15/16.46                   (((demorgan2a) =>
% 123.15/16.46                     (((demorgan2b2) =>
% 123.15/16.46                       (((demorgan2b) =>
% 123.15/16.46                         (((demorgan2) =>
% 123.15/16.46                           (((woz13rule0) =>
% 123.15/16.46                             (((woz13rule1) =>
% 123.15/16.46                               (((woz13rule2) =>
% 123.15/16.46                                 (((woz13rule3) =>
% 123.15/16.46                                   (((woz13rule4) =>
% 123.15/16.46                                     (((woz1_1) =>
% 123.15/16.46                                       (((woz1_2) =>
% 123.15/16.46                                         (((woz1_3) =>
% 123.15/16.46                                           (((woz1_4) =>
% 123.15/16.46                                             (((woz1_5) =>
% 123.15/16.46                                               (((breln1all2) =>
% 123.15/16.46                                                 (((breln1SetBreln1) =>
% 123.15/16.46                                                   (((choice2fnsingleton) =>
% 123.15/16.46                                                     (((setOfPairsIsBReln1) =>
% 123.15/16.46                                                       (((breln1all1) =>
% 123.15/16.46                                                         (((subbreln1) =>
% 123.15/16.46                                                           (((eqbreln1) =>
% 123.15/16.46                                                             (((breln1invprop) =>
% 123.15/16.46                                                               (((breln1invI) =>
% 123.15/16.46                                                                 (((breln1invE) =>
% 123.15/16.46                                                                   (((breln1compprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compEex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIL) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIR) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2459])).
% 123.15/16.46  thf(zip_derived_cl2481, plain,
% 123.15/16.46      (~ (((demorgan2a2) =>
% 123.15/16.46           (((demorgan1a) =>
% 123.15/16.46             (((demorgan1b) =>
% 123.15/16.46               (((demorgan1) =>
% 123.15/16.46                 (((demorgan2a) =>
% 123.15/16.46                   (((demorgan2b2) =>
% 123.15/16.46                     (((demorgan2b) =>
% 123.15/16.46                       (((demorgan2) =>
% 123.15/16.46                         (((woz13rule0) =>
% 123.15/16.46                           (((woz13rule1) =>
% 123.15/16.46                             (((woz13rule2) =>
% 123.15/16.46                               (((woz13rule3) =>
% 123.15/16.46                                 (((woz13rule4) =>
% 123.15/16.46                                   (((woz1_1) =>
% 123.15/16.46                                     (((woz1_2) =>
% 123.15/16.46                                       (((woz1_3) =>
% 123.15/16.46                                         (((woz1_4) =>
% 123.15/16.46                                           (((woz1_5) =>
% 123.15/16.46                                             (((breln1all2) =>
% 123.15/16.46                                               (((breln1SetBreln1) =>
% 123.15/16.46                                                 (((choice2fnsingleton) =>
% 123.15/16.46                                                   (((setOfPairsIsBReln1) =>
% 123.15/16.46                                                     (((breln1all1) =>
% 123.15/16.46                                                       (((subbreln1) =>
% 123.15/16.46                                                         (((eqbreln1) =>
% 123.15/16.46                                                           (((breln1invprop) =>
% 123.15/16.46                                                             (((breln1invI) =>
% 123.15/16.46                                                               (((breln1invE) =>
% 123.15/16.46                                                                 (((breln1compprop) =>
% 123.15/16.46                                                                   (((breln1compI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compEex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIL) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIR) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2470])).
% 123.15/16.46  thf(zip_derived_cl2493, plain,
% 123.15/16.46      (~ (((demorgan1a) =>
% 123.15/16.46           (((demorgan1b) =>
% 123.15/16.46             (((demorgan1) =>
% 123.15/16.46               (((demorgan2a) =>
% 123.15/16.46                 (((demorgan2b2) =>
% 123.15/16.46                   (((demorgan2b) =>
% 123.15/16.46                     (((demorgan2) =>
% 123.15/16.46                       (((woz13rule0) =>
% 123.15/16.46                         (((woz13rule1) =>
% 123.15/16.46                           (((woz13rule2) =>
% 123.15/16.46                             (((woz13rule3) =>
% 123.15/16.46                               (((woz13rule4) =>
% 123.15/16.46                                 (((woz1_1) =>
% 123.15/16.46                                   (((woz1_2) =>
% 123.15/16.46                                     (((woz1_3) =>
% 123.15/16.46                                       (((woz1_4) =>
% 123.15/16.46                                         (((woz1_5) =>
% 123.15/16.46                                           (((breln1all2) =>
% 123.15/16.46                                             (((breln1SetBreln1) =>
% 123.15/16.46                                               (((choice2fnsingleton) =>
% 123.15/16.46                                                 (((setOfPairsIsBReln1) =>
% 123.15/16.46                                                   (((breln1all1) =>
% 123.15/16.46                                                     (((subbreln1) =>
% 123.15/16.46                                                       (((eqbreln1) =>
% 123.15/16.46                                                         (((breln1invprop) =>
% 123.15/16.46                                                           (((breln1invI) =>
% 123.15/16.46                                                             (((breln1invE) =>
% 123.15/16.46                                                               (((breln1compprop) =>
% 123.15/16.46                                                                 (((breln1compI) =>
% 123.15/16.46                                                                   (((breln1compE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1compEex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIL) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIR) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2481])).
% 123.15/16.46  thf(zip_derived_cl2506, plain,
% 123.15/16.46      (~ (((demorgan1b) =>
% 123.15/16.46           (((demorgan1) =>
% 123.15/16.46             (((demorgan2a) =>
% 123.15/16.46               (((demorgan2b2) =>
% 123.15/16.46                 (((demorgan2b) =>
% 123.15/16.46                   (((demorgan2) =>
% 123.15/16.46                     (((woz13rule0) =>
% 123.15/16.46                       (((woz13rule1) =>
% 123.15/16.46                         (((woz13rule2) =>
% 123.15/16.46                           (((woz13rule3) =>
% 123.15/16.46                             (((woz13rule4) =>
% 123.15/16.46                               (((woz1_1) =>
% 123.15/16.46                                 (((woz1_2) =>
% 123.15/16.46                                   (((woz1_3) =>
% 123.15/16.46                                     (((woz1_4) =>
% 123.15/16.46                                       (((woz1_5) =>
% 123.15/16.46                                         (((breln1all2) =>
% 123.15/16.46                                           (((breln1SetBreln1) =>
% 123.15/16.46                                             (((choice2fnsingleton) =>
% 123.15/16.46                                               (((setOfPairsIsBReln1) =>
% 123.15/16.46                                                 (((breln1all1) =>
% 123.15/16.46                                                   (((subbreln1) =>
% 123.15/16.46                                                     (((eqbreln1) =>
% 123.15/16.46                                                       (((breln1invprop) =>
% 123.15/16.46                                                         (((breln1invI) =>
% 123.15/16.46                                                           (((breln1invE) =>
% 123.15/16.46                                                             (((breln1compprop) =>
% 123.15/16.46                                                               (((breln1compI) =>
% 123.15/16.46                                                                 (((breln1compE) =>
% 123.15/16.46                                                                   (((breln1compEex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIL) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIR) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2493])).
% 123.15/16.46  thf(zip_derived_cl2518, plain,
% 123.15/16.46      (~ (((demorgan1) =>
% 123.15/16.46           (((demorgan2a) =>
% 123.15/16.46             (((demorgan2b2) =>
% 123.15/16.46               (((demorgan2b) =>
% 123.15/16.46                 (((demorgan2) =>
% 123.15/16.46                   (((woz13rule0) =>
% 123.15/16.46                     (((woz13rule1) =>
% 123.15/16.46                       (((woz13rule2) =>
% 123.15/16.46                         (((woz13rule3) =>
% 123.15/16.46                           (((woz13rule4) =>
% 123.15/16.46                             (((woz1_1) =>
% 123.15/16.46                               (((woz1_2) =>
% 123.15/16.46                                 (((woz1_3) =>
% 123.15/16.46                                   (((woz1_4) =>
% 123.15/16.46                                     (((woz1_5) =>
% 123.15/16.46                                       (((breln1all2) =>
% 123.15/16.46                                         (((breln1SetBreln1) =>
% 123.15/16.46                                           (((choice2fnsingleton) =>
% 123.15/16.46                                             (((setOfPairsIsBReln1) =>
% 123.15/16.46                                               (((breln1all1) =>
% 123.15/16.46                                                 (((subbreln1) =>
% 123.15/16.46                                                   (((eqbreln1) =>
% 123.15/16.46                                                     (((breln1invprop) =>
% 123.15/16.46                                                       (((breln1invI) =>
% 123.15/16.46                                                         (((breln1invE) =>
% 123.15/16.46                                                           (((breln1compprop) =>
% 123.15/16.46                                                             (((breln1compI) =>
% 123.15/16.46                                                               (((breln1compE) =>
% 123.15/16.46                                                                 (((breln1compEex) =>
% 123.15/16.46                                                                   (((breln1unionprop) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIL) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIR) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2506])).
% 123.15/16.46  thf(zip_derived_cl2530, plain,
% 123.15/16.46      (~ (((demorgan2a) =>
% 123.15/16.46           (((demorgan2b2) =>
% 123.15/16.46             (((demorgan2b) =>
% 123.15/16.46               (((demorgan2) =>
% 123.15/16.46                 (((woz13rule0) =>
% 123.15/16.46                   (((woz13rule1) =>
% 123.15/16.46                     (((woz13rule2) =>
% 123.15/16.46                       (((woz13rule3) =>
% 123.15/16.46                         (((woz13rule4) =>
% 123.15/16.46                           (((woz1_1) =>
% 123.15/16.46                             (((woz1_2) =>
% 123.15/16.46                               (((woz1_3) =>
% 123.15/16.46                                 (((woz1_4) =>
% 123.15/16.46                                   (((woz1_5) =>
% 123.15/16.46                                     (((breln1all2) =>
% 123.15/16.46                                       (((breln1SetBreln1) =>
% 123.15/16.46                                         (((choice2fnsingleton) =>
% 123.15/16.46                                           (((setOfPairsIsBReln1) =>
% 123.15/16.46                                             (((breln1all1) =>
% 123.15/16.46                                               (((subbreln1) =>
% 123.15/16.46                                                 (((eqbreln1) =>
% 123.15/16.46                                                   (((breln1invprop) =>
% 123.15/16.46                                                     (((breln1invI) =>
% 123.15/16.46                                                       (((breln1invE) =>
% 123.15/16.46                                                         (((breln1compprop) =>
% 123.15/16.46                                                           (((breln1compI) =>
% 123.15/16.46                                                             (((breln1compE) =>
% 123.15/16.46                                                               (((breln1compEex) =>
% 123.15/16.46                                                                 (((breln1unionprop) =>
% 123.15/16.46                                                                   (((breln1unionIL) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionIR) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2518])).
% 123.15/16.46  thf(zip_derived_cl2541, plain,
% 123.15/16.46      (~ (((demorgan2b2) =>
% 123.15/16.46           (((demorgan2b) =>
% 123.15/16.46             (((demorgan2) =>
% 123.15/16.46               (((woz13rule0) =>
% 123.15/16.46                 (((woz13rule1) =>
% 123.15/16.46                   (((woz13rule2) =>
% 123.15/16.46                     (((woz13rule3) =>
% 123.15/16.46                       (((woz13rule4) =>
% 123.15/16.46                         (((woz1_1) =>
% 123.15/16.46                           (((woz1_2) =>
% 123.15/16.46                             (((woz1_3) =>
% 123.15/16.46                               (((woz1_4) =>
% 123.15/16.46                                 (((woz1_5) =>
% 123.15/16.46                                   (((breln1all2) =>
% 123.15/16.46                                     (((breln1SetBreln1) =>
% 123.15/16.46                                       (((choice2fnsingleton) =>
% 123.15/16.46                                         (((setOfPairsIsBReln1) =>
% 123.15/16.46                                           (((breln1all1) =>
% 123.15/16.46                                             (((subbreln1) =>
% 123.15/16.46                                               (((eqbreln1) =>
% 123.15/16.46                                                 (((breln1invprop) =>
% 123.15/16.46                                                   (((breln1invI) =>
% 123.15/16.46                                                     (((breln1invE) =>
% 123.15/16.46                                                       (((breln1compprop) =>
% 123.15/16.46                                                         (((breln1compI) =>
% 123.15/16.46                                                           (((breln1compE) =>
% 123.15/16.46                                                             (((breln1compEex) =>
% 123.15/16.46                                                               (((breln1unionprop) =>
% 123.15/16.46                                                                 (((breln1unionIL) =>
% 123.15/16.46                                                                   (((breln1unionIR) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2530])).
% 123.15/16.46  thf(zip_derived_cl2552, plain,
% 123.15/16.46      (~ (((demorgan2b) =>
% 123.15/16.46           (((demorgan2) =>
% 123.15/16.46             (((woz13rule0) =>
% 123.15/16.46               (((woz13rule1) =>
% 123.15/16.46                 (((woz13rule2) =>
% 123.15/16.46                   (((woz13rule3) =>
% 123.15/16.46                     (((woz13rule4) =>
% 123.15/16.46                       (((woz1_1) =>
% 123.15/16.46                         (((woz1_2) =>
% 123.15/16.46                           (((woz1_3) =>
% 123.15/16.46                             (((woz1_4) =>
% 123.15/16.46                               (((woz1_5) =>
% 123.15/16.46                                 (((breln1all2) =>
% 123.15/16.46                                   (((breln1SetBreln1) =>
% 123.15/16.46                                     (((choice2fnsingleton) =>
% 123.15/16.46                                       (((setOfPairsIsBReln1) =>
% 123.15/16.46                                         (((breln1all1) =>
% 123.15/16.46                                           (((subbreln1) =>
% 123.15/16.46                                             (((eqbreln1) =>
% 123.15/16.46                                               (((breln1invprop) =>
% 123.15/16.46                                                 (((breln1invI) =>
% 123.15/16.46                                                   (((breln1invE) =>
% 123.15/16.46                                                     (((breln1compprop) =>
% 123.15/16.46                                                       (((breln1compI) =>
% 123.15/16.46                                                         (((breln1compE) =>
% 123.15/16.46                                                           (((breln1compEex) =>
% 123.15/16.46                                                             (((breln1unionprop) =>
% 123.15/16.46                                                               (((breln1unionIL) =>
% 123.15/16.46                                                                 (((breln1unionIR) =>
% 123.15/16.46                                                                   (((breln1unionI) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2541])).
% 123.15/16.46  thf(zip_derived_cl2563, plain,
% 123.15/16.46      (~ (((demorgan2) =>
% 123.15/16.46           (((woz13rule0) =>
% 123.15/16.46             (((woz13rule1) =>
% 123.15/16.46               (((woz13rule2) =>
% 123.15/16.46                 (((woz13rule3) =>
% 123.15/16.46                   (((woz13rule4) =>
% 123.15/16.46                     (((woz1_1) =>
% 123.15/16.46                       (((woz1_2) =>
% 123.15/16.46                         (((woz1_3) =>
% 123.15/16.46                           (((woz1_4) =>
% 123.15/16.46                             (((woz1_5) =>
% 123.15/16.46                               (((breln1all2) =>
% 123.15/16.46                                 (((breln1SetBreln1) =>
% 123.15/16.46                                   (((choice2fnsingleton) =>
% 123.15/16.46                                     (((setOfPairsIsBReln1) =>
% 123.15/16.46                                       (((breln1all1) =>
% 123.15/16.46                                         (((subbreln1) =>
% 123.15/16.46                                           (((eqbreln1) =>
% 123.15/16.46                                             (((breln1invprop) =>
% 123.15/16.46                                               (((breln1invI) =>
% 123.15/16.46                                                 (((breln1invE) =>
% 123.15/16.46                                                   (((breln1compprop) =>
% 123.15/16.46                                                     (((breln1compI) =>
% 123.15/16.46                                                       (((breln1compE) =>
% 123.15/16.46                                                         (((breln1compEex) =>
% 123.15/16.46                                                           (((breln1unionprop) =>
% 123.15/16.46                                                             (((breln1unionIL) =>
% 123.15/16.46                                                               (((breln1unionIR) =>
% 123.15/16.46                                                                 (((breln1unionI) =>
% 123.15/16.46                                                                   (((breln1unionE) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2552])).
% 123.15/16.46  thf(zip_derived_cl2575, plain,
% 123.15/16.46      (~ (((woz13rule0) =>
% 123.15/16.46           (((woz13rule1) =>
% 123.15/16.46             (((woz13rule2) =>
% 123.15/16.46               (((woz13rule3) =>
% 123.15/16.46                 (((woz13rule4) =>
% 123.15/16.46                   (((woz1_1) =>
% 123.15/16.46                     (((woz1_2) =>
% 123.15/16.46                       (((woz1_3) =>
% 123.15/16.46                         (((woz1_4) =>
% 123.15/16.46                           (((woz1_5) =>
% 123.15/16.46                             (((breln1all2) =>
% 123.15/16.46                               (((breln1SetBreln1) =>
% 123.15/16.46                                 (((choice2fnsingleton) =>
% 123.15/16.46                                   (((setOfPairsIsBReln1) =>
% 123.15/16.46                                     (((breln1all1) =>
% 123.15/16.46                                       (((subbreln1) =>
% 123.15/16.46                                         (((eqbreln1) =>
% 123.15/16.46                                           (((breln1invprop) =>
% 123.15/16.46                                             (((breln1invI) =>
% 123.15/16.46                                               (((breln1invE) =>
% 123.15/16.46                                                 (((breln1compprop) =>
% 123.15/16.46                                                   (((breln1compI) =>
% 123.15/16.46                                                     (((breln1compE) =>
% 123.15/16.46                                                       (((breln1compEex) =>
% 123.15/16.46                                                         (((breln1unionprop) =>
% 123.15/16.46                                                           (((breln1unionIL) =>
% 123.15/16.46                                                             (((breln1unionIR) =>
% 123.15/16.46                                                               (((breln1unionI) =>
% 123.15/16.46                                                                 (((breln1unionE) =>
% 123.15/16.46                                                                   (((breln1unionEcases) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2563])).
% 123.15/16.46  thf(zip_derived_cl2586, plain,
% 123.15/16.46      (~ (((woz13rule1) =>
% 123.15/16.46           (((woz13rule2) =>
% 123.15/16.46             (((woz13rule3) =>
% 123.15/16.46               (((woz13rule4) =>
% 123.15/16.46                 (((woz1_1) =>
% 123.15/16.46                   (((woz1_2) =>
% 123.15/16.46                     (((woz1_3) =>
% 123.15/16.46                       (((woz1_4) =>
% 123.15/16.46                         (((woz1_5) =>
% 123.15/16.46                           (((breln1all2) =>
% 123.15/16.46                             (((breln1SetBreln1) =>
% 123.15/16.46                               (((choice2fnsingleton) =>
% 123.15/16.46                                 (((setOfPairsIsBReln1) =>
% 123.15/16.46                                   (((breln1all1) =>
% 123.15/16.46                                     (((subbreln1) =>
% 123.15/16.46                                       (((eqbreln1) =>
% 123.15/16.46                                         (((breln1invprop) =>
% 123.15/16.46                                           (((breln1invI) =>
% 123.15/16.46                                             (((breln1invE) =>
% 123.15/16.46                                               (((breln1compprop) =>
% 123.15/16.46                                                 (((breln1compI) =>
% 123.15/16.46                                                   (((breln1compE) =>
% 123.15/16.46                                                     (((breln1compEex) =>
% 123.15/16.46                                                       (((breln1unionprop) =>
% 123.15/16.46                                                         (((breln1unionIL) =>
% 123.15/16.46                                                           (((breln1unionIR) =>
% 123.15/16.46                                                             (((breln1unionI) =>
% 123.15/16.46                                                               (((breln1unionE) =>
% 123.15/16.46                                                                 (((breln1unionEcases) =>
% 123.15/16.46                                                                   (((breln1unionCommutes) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2575])).
% 123.15/16.46  thf(zip_derived_cl2599, plain,
% 123.15/16.46      (~ (((woz13rule2) =>
% 123.15/16.46           (((woz13rule3) =>
% 123.15/16.46             (((woz13rule4) =>
% 123.15/16.46               (((woz1_1) =>
% 123.15/16.46                 (((woz1_2) =>
% 123.15/16.46                   (((woz1_3) =>
% 123.15/16.46                     (((woz1_4) =>
% 123.15/16.46                       (((woz1_5) =>
% 123.15/16.46                         (((breln1all2) =>
% 123.15/16.46                           (((breln1SetBreln1) =>
% 123.15/16.46                             (((choice2fnsingleton) =>
% 123.15/16.46                               (((setOfPairsIsBReln1) =>
% 123.15/16.46                                 (((breln1all1) =>
% 123.15/16.46                                   (((subbreln1) =>
% 123.15/16.46                                     (((eqbreln1) =>
% 123.15/16.46                                       (((breln1invprop) =>
% 123.15/16.46                                         (((breln1invI) =>
% 123.15/16.46                                           (((breln1invE) =>
% 123.15/16.46                                             (((breln1compprop) =>
% 123.15/16.46                                               (((breln1compI) =>
% 123.15/16.46                                                 (((breln1compE) =>
% 123.15/16.46                                                   (((breln1compEex) =>
% 123.15/16.46                                                     (((breln1unionprop) =>
% 123.15/16.46                                                       (((breln1unionIL) =>
% 123.15/16.46                                                         (((breln1unionIR) =>
% 123.15/16.46                                                           (((breln1unionI) =>
% 123.15/16.46                                                             (((breln1unionE) =>
% 123.15/16.46                                                               (((breln1unionEcases) =>
% 123.15/16.46                                                                 (((breln1unionCommutes) =>
% 123.15/16.46                                                                   (((woz2Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2586])).
% 123.15/16.46  thf(zip_derived_cl2610, plain,
% 123.15/16.46      (~ (((woz13rule3) =>
% 123.15/16.46           (((woz13rule4) =>
% 123.15/16.46             (((woz1_1) =>
% 123.15/16.46               (((woz1_2) =>
% 123.15/16.46                 (((woz1_3) =>
% 123.15/16.46                   (((woz1_4) =>
% 123.15/16.46                     (((woz1_5) =>
% 123.15/16.46                       (((breln1all2) =>
% 123.15/16.46                         (((breln1SetBreln1) =>
% 123.15/16.46                           (((choice2fnsingleton) =>
% 123.15/16.46                             (((setOfPairsIsBReln1) =>
% 123.15/16.46                               (((breln1all1) =>
% 123.15/16.46                                 (((subbreln1) =>
% 123.15/16.46                                   (((eqbreln1) =>
% 123.15/16.46                                     (((breln1invprop) =>
% 123.15/16.46                                       (((breln1invI) =>
% 123.15/16.46                                         (((breln1invE) =>
% 123.15/16.46                                           (((breln1compprop) =>
% 123.15/16.46                                             (((breln1compI) =>
% 123.15/16.46                                               (((breln1compE) =>
% 123.15/16.46                                                 (((breln1compEex) =>
% 123.15/16.46                                                   (((breln1unionprop) =>
% 123.15/16.46                                                     (((breln1unionIL) =>
% 123.15/16.46                                                       (((breln1unionIR) =>
% 123.15/16.46                                                         (((breln1unionI) =>
% 123.15/16.46                                                           (((breln1unionE) =>
% 123.15/16.46                                                             (((breln1unionEcases) =>
% 123.15/16.46                                                               (((breln1unionCommutes) =>
% 123.15/16.46                                                                 (((woz2Ex) =>
% 123.15/16.46                                                                   (((woz2W) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2599])).
% 123.15/16.46  thf(zip_derived_cl2620, plain,
% 123.15/16.46      (~ (((woz13rule4) =>
% 123.15/16.46           (((woz1_1) =>
% 123.15/16.46             (((woz1_2) =>
% 123.15/16.46               (((woz1_3) =>
% 123.15/16.46                 (((woz1_4) =>
% 123.15/16.46                   (((woz1_5) =>
% 123.15/16.46                     (((breln1all2) =>
% 123.15/16.46                       (((breln1SetBreln1) =>
% 123.15/16.46                         (((choice2fnsingleton) =>
% 123.15/16.46                           (((setOfPairsIsBReln1) =>
% 123.15/16.46                             (((breln1all1) =>
% 123.15/16.46                               (((subbreln1) =>
% 123.15/16.46                                 (((eqbreln1) =>
% 123.15/16.46                                   (((breln1invprop) =>
% 123.15/16.46                                     (((breln1invI) =>
% 123.15/16.46                                       (((breln1invE) =>
% 123.15/16.46                                         (((breln1compprop) =>
% 123.15/16.46                                           (((breln1compI) =>
% 123.15/16.46                                             (((breln1compE) =>
% 123.15/16.46                                               (((breln1compEex) =>
% 123.15/16.46                                                 (((breln1unionprop) =>
% 123.15/16.46                                                   (((breln1unionIL) =>
% 123.15/16.46                                                     (((breln1unionIR) =>
% 123.15/16.46                                                       (((breln1unionI) =>
% 123.15/16.46                                                         (((breln1unionE) =>
% 123.15/16.46                                                           (((breln1unionEcases) =>
% 123.15/16.46                                                             (((breln1unionCommutes) =>
% 123.15/16.46                                                               (((woz2Ex) =>
% 123.15/16.46                                                                 (((woz2W) =>
% 123.15/16.46                                                                   (((woz2A) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2610])).
% 123.15/16.46  thf(zip_derived_cl2630, plain,
% 123.15/16.46      (~ (((woz1_1) =>
% 123.15/16.46           (((woz1_2) =>
% 123.15/16.46             (((woz1_3) =>
% 123.15/16.46               (((woz1_4) =>
% 123.15/16.46                 (((woz1_5) =>
% 123.15/16.46                   (((breln1all2) =>
% 123.15/16.46                     (((breln1SetBreln1) =>
% 123.15/16.46                       (((choice2fnsingleton) =>
% 123.15/16.46                         (((setOfPairsIsBReln1) =>
% 123.15/16.46                           (((breln1all1) =>
% 123.15/16.46                             (((subbreln1) =>
% 123.15/16.46                               (((eqbreln1) =>
% 123.15/16.46                                 (((breln1invprop) =>
% 123.15/16.46                                   (((breln1invI) =>
% 123.15/16.46                                     (((breln1invE) =>
% 123.15/16.46                                       (((breln1compprop) =>
% 123.15/16.46                                         (((breln1compI) =>
% 123.15/16.46                                           (((breln1compE) =>
% 123.15/16.46                                             (((breln1compEex) =>
% 123.15/16.46                                               (((breln1unionprop) =>
% 123.15/16.46                                                 (((breln1unionIL) =>
% 123.15/16.46                                                   (((breln1unionIR) =>
% 123.15/16.46                                                     (((breln1unionI) =>
% 123.15/16.46                                                       (((breln1unionE) =>
% 123.15/16.46                                                         (((breln1unionEcases) =>
% 123.15/16.46                                                           (((breln1unionCommutes) =>
% 123.15/16.46                                                             (((woz2Ex) =>
% 123.15/16.46                                                               (((woz2W) =>
% 123.15/16.46                                                                 (((woz2A) =>
% 123.15/16.46                                                                   (((woz2B) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2620])).
% 123.15/16.46  thf(zip_derived_cl2641, plain,
% 123.15/16.46      (~ (((woz1_2) =>
% 123.15/16.46           (((woz1_3) =>
% 123.15/16.46             (((woz1_4) =>
% 123.15/16.46               (((woz1_5) =>
% 123.15/16.46                 (((breln1all2) =>
% 123.15/16.46                   (((breln1SetBreln1) =>
% 123.15/16.46                     (((choice2fnsingleton) =>
% 123.15/16.46                       (((setOfPairsIsBReln1) =>
% 123.15/16.46                         (((breln1all1) =>
% 123.15/16.46                           (((subbreln1) =>
% 123.15/16.46                             (((eqbreln1) =>
% 123.15/16.46                               (((breln1invprop) =>
% 123.15/16.46                                 (((breln1invI) =>
% 123.15/16.46                                   (((breln1invE) =>
% 123.15/16.46                                     (((breln1compprop) =>
% 123.15/16.46                                       (((breln1compI) =>
% 123.15/16.46                                         (((breln1compE) =>
% 123.15/16.46                                           (((breln1compEex) =>
% 123.15/16.46                                             (((breln1unionprop) =>
% 123.15/16.46                                               (((breln1unionIL) =>
% 123.15/16.46                                                 (((breln1unionIR) =>
% 123.15/16.46                                                   (((breln1unionI) =>
% 123.15/16.46                                                     (((breln1unionE) =>
% 123.15/16.46                                                       (((breln1unionEcases) =>
% 123.15/16.46                                                         (((breln1unionCommutes) =>
% 123.15/16.46                                                           (((woz2Ex) =>
% 123.15/16.46                                                             (((woz2W) =>
% 123.15/16.46                                                               (((woz2A) =>
% 123.15/16.46                                                                 (((woz2B) =>
% 123.15/16.46                                                                   (((image1Ex) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2630])).
% 123.15/16.46  thf(zip_derived_cl2652, plain,
% 123.15/16.46      (~ (((woz1_3) =>
% 123.15/16.46           (((woz1_4) =>
% 123.15/16.46             (((woz1_5) =>
% 123.15/16.46               (((breln1all2) =>
% 123.15/16.46                 (((breln1SetBreln1) =>
% 123.15/16.46                   (((choice2fnsingleton) =>
% 123.15/16.46                     (((setOfPairsIsBReln1) =>
% 123.15/16.46                       (((breln1all1) =>
% 123.15/16.46                         (((subbreln1) =>
% 123.15/16.46                           (((eqbreln1) =>
% 123.15/16.46                             (((breln1invprop) =>
% 123.15/16.46                               (((breln1invI) =>
% 123.15/16.46                                 (((breln1invE) =>
% 123.15/16.46                                   (((breln1compprop) =>
% 123.15/16.46                                     (((breln1compI) =>
% 123.15/16.46                                       (((breln1compE) =>
% 123.15/16.46                                         (((breln1compEex) =>
% 123.15/16.46                                           (((breln1unionprop) =>
% 123.15/16.46                                             (((breln1unionIL) =>
% 123.15/16.46                                               (((breln1unionIR) =>
% 123.15/16.46                                                 (((breln1unionI) =>
% 123.15/16.46                                                   (((breln1unionE) =>
% 123.15/16.46                                                     (((breln1unionEcases) =>
% 123.15/16.46                                                       (((breln1unionCommutes) =>
% 123.15/16.46                                                         (((woz2Ex) =>
% 123.15/16.46                                                           (((woz2W) =>
% 123.15/16.46                                                             (((woz2A) =>
% 123.15/16.46                                                               (((woz2B) =>
% 123.15/16.46                                                                 (((image1Ex) =>
% 123.15/16.46                                                                   (((image1Ex1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2641])).
% 123.15/16.46  thf(zip_derived_cl2663, plain,
% 123.15/16.46      (~ (((woz1_4) =>
% 123.15/16.46           (((woz1_5) =>
% 123.15/16.46             (((breln1all2) =>
% 123.15/16.46               (((breln1SetBreln1) =>
% 123.15/16.46                 (((choice2fnsingleton) =>
% 123.15/16.46                   (((setOfPairsIsBReln1) =>
% 123.15/16.46                     (((breln1all1) =>
% 123.15/16.46                       (((subbreln1) =>
% 123.15/16.46                         (((eqbreln1) =>
% 123.15/16.46                           (((breln1invprop) =>
% 123.15/16.46                             (((breln1invI) =>
% 123.15/16.46                               (((breln1invE) =>
% 123.15/16.46                                 (((breln1compprop) =>
% 123.15/16.46                                   (((breln1compI) =>
% 123.15/16.46                                     (((breln1compE) =>
% 123.15/16.46                                       (((breln1compEex) =>
% 123.15/16.46                                         (((breln1unionprop) =>
% 123.15/16.46                                           (((breln1unionIL) =>
% 123.15/16.46                                             (((breln1unionIR) =>
% 123.15/16.46                                               (((breln1unionI) =>
% 123.15/16.46                                                 (((breln1unionE) =>
% 123.15/16.46                                                   (((breln1unionEcases) =>
% 123.15/16.46                                                     (((breln1unionCommutes) =>
% 123.15/16.46                                                       (((woz2Ex) =>
% 123.15/16.46                                                         (((woz2W) =>
% 123.15/16.46                                                           (((woz2A) =>
% 123.15/16.46                                                             (((woz2B) =>
% 123.15/16.46                                                               (((image1Ex) =>
% 123.15/16.46                                                                 (((image1Ex1) =>
% 123.15/16.46                                                                   (((image1Equiv) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2652])).
% 123.15/16.46  thf(zip_derived_cl2672, plain,
% 123.15/16.46      (~ (((woz1_5) =>
% 123.15/16.46           (((breln1all2) =>
% 123.15/16.46             (((breln1SetBreln1) =>
% 123.15/16.46               (((choice2fnsingleton) =>
% 123.15/16.46                 (((setOfPairsIsBReln1) =>
% 123.15/16.46                   (((breln1all1) =>
% 123.15/16.46                     (((subbreln1) =>
% 123.15/16.46                       (((eqbreln1) =>
% 123.15/16.46                         (((breln1invprop) =>
% 123.15/16.46                           (((breln1invI) =>
% 123.15/16.46                             (((breln1invE) =>
% 123.15/16.46                               (((breln1compprop) =>
% 123.15/16.46                                 (((breln1compI) =>
% 123.15/16.46                                   (((breln1compE) =>
% 123.15/16.46                                     (((breln1compEex) =>
% 123.15/16.46                                       (((breln1unionprop) =>
% 123.15/16.46                                         (((breln1unionIL) =>
% 123.15/16.46                                           (((breln1unionIR) =>
% 123.15/16.46                                             (((breln1unionI) =>
% 123.15/16.46                                               (((breln1unionE) =>
% 123.15/16.46                                                 (((breln1unionEcases) =>
% 123.15/16.46                                                   (((breln1unionCommutes) =>
% 123.15/16.46                                                     (((woz2Ex) =>
% 123.15/16.46                                                       (((woz2W) =>
% 123.15/16.46                                                         (((woz2A) =>
% 123.15/16.46                                                           (((woz2B) =>
% 123.15/16.46                                                             (((image1Ex) =>
% 123.15/16.46                                                               (((image1Ex1) =>
% 123.15/16.46                                                                 (((image1Equiv) =>
% 123.15/16.46                                                                   (((image1E) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2663])).
% 123.15/16.46  thf(zip_derived_cl2682, plain,
% 123.15/16.46      (~ (((breln1all2) =>
% 123.15/16.46           (((breln1SetBreln1) =>
% 123.15/16.46             (((choice2fnsingleton) =>
% 123.15/16.46               (((setOfPairsIsBReln1) =>
% 123.15/16.46                 (((breln1all1) =>
% 123.15/16.46                   (((subbreln1) =>
% 123.15/16.46                     (((eqbreln1) =>
% 123.15/16.46                       (((breln1invprop) =>
% 123.15/16.46                         (((breln1invI) =>
% 123.15/16.46                           (((breln1invE) =>
% 123.15/16.46                             (((breln1compprop) =>
% 123.15/16.46                               (((breln1compI) =>
% 123.15/16.46                                 (((breln1compE) =>
% 123.15/16.46                                   (((breln1compEex) =>
% 123.15/16.46                                     (((breln1unionprop) =>
% 123.15/16.46                                       (((breln1unionIL) =>
% 123.15/16.46                                         (((breln1unionIR) =>
% 123.15/16.46                                           (((breln1unionI) =>
% 123.15/16.46                                             (((breln1unionE) =>
% 123.15/16.46                                               (((breln1unionEcases) =>
% 123.15/16.46                                                 (((breln1unionCommutes) =>
% 123.15/16.46                                                   (((woz2Ex) =>
% 123.15/16.46                                                     (((woz2W) =>
% 123.15/16.46                                                       (((woz2A) =>
% 123.15/16.46                                                         (((woz2B) =>
% 123.15/16.46                                                           (((image1Ex) =>
% 123.15/16.46                                                             (((image1Ex1) =>
% 123.15/16.46                                                               (((image1Equiv) =>
% 123.15/16.46                                                                 (((image1E) =>
% 123.15/16.46                                                                   (((image1I) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2672])).
% 123.15/16.46  thf(zip_derived_cl2693, plain,
% 123.15/16.46      (~ (((breln1SetBreln1) =>
% 123.15/16.46           (((choice2fnsingleton) =>
% 123.15/16.46             (((setOfPairsIsBReln1) =>
% 123.15/16.46               (((breln1all1) =>
% 123.15/16.46                 (((subbreln1) =>
% 123.15/16.46                   (((eqbreln1) =>
% 123.15/16.46                     (((breln1invprop) =>
% 123.15/16.46                       (((breln1invI) =>
% 123.15/16.46                         (((breln1invE) =>
% 123.15/16.46                           (((breln1compprop) =>
% 123.15/16.46                             (((breln1compI) =>
% 123.15/16.46                               (((breln1compE) =>
% 123.15/16.46                                 (((breln1compEex) =>
% 123.15/16.46                                   (((breln1unionprop) =>
% 123.15/16.46                                     (((breln1unionIL) =>
% 123.15/16.46                                       (((breln1unionIR) =>
% 123.15/16.46                                         (((breln1unionI) =>
% 123.15/16.46                                           (((breln1unionE) =>
% 123.15/16.46                                             (((breln1unionEcases) =>
% 123.15/16.46                                               (((breln1unionCommutes) =>
% 123.15/16.46                                                 (((woz2Ex) =>
% 123.15/16.46                                                   (((woz2W) =>
% 123.15/16.46                                                     (((woz2A) =>
% 123.15/16.46                                                       (((woz2B) =>
% 123.15/16.46                                                         (((image1Ex) =>
% 123.15/16.46                                                           (((image1Ex1) =>
% 123.15/16.46                                                             (((image1Equiv) =>
% 123.15/16.46                                                               (((image1E) =>
% 123.15/16.46                                                                 (((image1I) =>
% 123.15/16.46                                                                   (((injFuncInInjFuncSet) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2682])).
% 123.15/16.46  thf(zip_derived_cl2704, plain,
% 123.15/16.46      (~ (((choice2fnsingleton) =>
% 123.15/16.46           (((setOfPairsIsBReln1) =>
% 123.15/16.46             (((breln1all1) =>
% 123.15/16.46               (((subbreln1) =>
% 123.15/16.46                 (((eqbreln1) =>
% 123.15/16.46                   (((breln1invprop) =>
% 123.15/16.46                     (((breln1invI) =>
% 123.15/16.46                       (((breln1invE) =>
% 123.15/16.46                         (((breln1compprop) =>
% 123.15/16.46                           (((breln1compI) =>
% 123.15/16.46                             (((breln1compE) =>
% 123.15/16.46                               (((breln1compEex) =>
% 123.15/16.46                                 (((breln1unionprop) =>
% 123.15/16.46                                   (((breln1unionIL) =>
% 123.15/16.46                                     (((breln1unionIR) =>
% 123.15/16.46                                       (((breln1unionI) =>
% 123.15/16.46                                         (((breln1unionE) =>
% 123.15/16.46                                           (((breln1unionEcases) =>
% 123.15/16.46                                             (((breln1unionCommutes) =>
% 123.15/16.46                                               (((woz2Ex) =>
% 123.15/16.46                                                 (((woz2W) =>
% 123.15/16.46                                                   (((woz2A) =>
% 123.15/16.46                                                     (((woz2B) =>
% 123.15/16.46                                                       (((image1Ex) =>
% 123.15/16.46                                                         (((image1Ex1) =>
% 123.15/16.46                                                           (((image1Equiv) =>
% 123.15/16.46                                                             (((image1E) =>
% 123.15/16.46                                                               (((image1I) =>
% 123.15/16.46                                                                 (((injFuncInInjFuncSet) =>
% 123.15/16.46                                                                   (((injFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2693])).
% 123.15/16.46  thf(zip_derived_cl2714, plain,
% 123.15/16.46      (~ (((setOfPairsIsBReln1) =>
% 123.15/16.46           (((breln1all1) =>
% 123.15/16.46             (((subbreln1) =>
% 123.15/16.46               (((eqbreln1) =>
% 123.15/16.46                 (((breln1invprop) =>
% 123.15/16.46                   (((breln1invI) =>
% 123.15/16.46                     (((breln1invE) =>
% 123.15/16.46                       (((breln1compprop) =>
% 123.15/16.46                         (((breln1compI) =>
% 123.15/16.46                           (((breln1compE) =>
% 123.15/16.46                             (((breln1compEex) =>
% 123.15/16.46                               (((breln1unionprop) =>
% 123.15/16.46                                 (((breln1unionIL) =>
% 123.15/16.46                                   (((breln1unionIR) =>
% 123.15/16.46                                     (((breln1unionI) =>
% 123.15/16.46                                       (((breln1unionE) =>
% 123.15/16.46                                         (((breln1unionEcases) =>
% 123.15/16.46                                           (((breln1unionCommutes) =>
% 123.15/16.46                                             (((woz2Ex) =>
% 123.15/16.46                                               (((woz2W) =>
% 123.15/16.46                                                 (((woz2A) =>
% 123.15/16.46                                                   (((woz2B) =>
% 123.15/16.46                                                     (((image1Ex) =>
% 123.15/16.46                                                       (((image1Ex1) =>
% 123.15/16.46                                                         (((image1Equiv) =>
% 123.15/16.46                                                           (((image1E) =>
% 123.15/16.46                                                             (((image1I) =>
% 123.15/16.46                                                               (((injFuncInInjFuncSet) =>
% 123.15/16.46                                                                 (((injFuncSetFuncIn) =>
% 123.15/16.46                                                                   (((injFuncSetFuncInj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2704])).
% 123.15/16.46  thf(zip_derived_cl2725, plain,
% 123.15/16.46      (~ (((breln1all1) =>
% 123.15/16.46           (((subbreln1) =>
% 123.15/16.46             (((eqbreln1) =>
% 123.15/16.46               (((breln1invprop) =>
% 123.15/16.46                 (((breln1invI) =>
% 123.15/16.46                   (((breln1invE) =>
% 123.15/16.46                     (((breln1compprop) =>
% 123.15/16.46                       (((breln1compI) =>
% 123.15/16.46                         (((breln1compE) =>
% 123.15/16.46                           (((breln1compEex) =>
% 123.15/16.46                             (((breln1unionprop) =>
% 123.15/16.46                               (((breln1unionIL) =>
% 123.15/16.46                                 (((breln1unionIR) =>
% 123.15/16.46                                   (((breln1unionI) =>
% 123.15/16.46                                     (((breln1unionE) =>
% 123.15/16.46                                       (((breln1unionEcases) =>
% 123.15/16.46                                         (((breln1unionCommutes) =>
% 123.15/16.46                                           (((woz2Ex) =>
% 123.15/16.46                                             (((woz2W) =>
% 123.15/16.46                                               (((woz2A) =>
% 123.15/16.46                                                 (((woz2B) =>
% 123.15/16.46                                                   (((image1Ex) =>
% 123.15/16.46                                                     (((image1Ex1) =>
% 123.15/16.46                                                       (((image1Equiv) =>
% 123.15/16.46                                                         (((image1E) =>
% 123.15/16.46                                                           (((image1I) =>
% 123.15/16.46                                                             (((injFuncInInjFuncSet) =>
% 123.15/16.46                                                               (((injFuncSetFuncIn) =>
% 123.15/16.46                                                                 (((injFuncSetFuncInj) =>
% 123.15/16.46                                                                   (((surjFuncSetFuncIn) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2714])).
% 123.15/16.46  thf(zip_derived_cl2736, plain,
% 123.15/16.46      (~ (((subbreln1) =>
% 123.15/16.46           (((eqbreln1) =>
% 123.15/16.46             (((breln1invprop) =>
% 123.15/16.46               (((breln1invI) =>
% 123.15/16.46                 (((breln1invE) =>
% 123.15/16.46                   (((breln1compprop) =>
% 123.15/16.46                     (((breln1compI) =>
% 123.15/16.46                       (((breln1compE) =>
% 123.15/16.46                         (((breln1compEex) =>
% 123.15/16.46                           (((breln1unionprop) =>
% 123.15/16.46                             (((breln1unionIL) =>
% 123.15/16.46                               (((breln1unionIR) =>
% 123.15/16.46                                 (((breln1unionI) =>
% 123.15/16.46                                   (((breln1unionE) =>
% 123.15/16.46                                     (((breln1unionEcases) =>
% 123.15/16.46                                       (((breln1unionCommutes) =>
% 123.15/16.46                                         (((woz2Ex) =>
% 123.15/16.46                                           (((woz2W) =>
% 123.15/16.46                                             (((woz2A) =>
% 123.15/16.46                                               (((woz2B) =>
% 123.15/16.46                                                 (((image1Ex) =>
% 123.15/16.46                                                   (((image1Ex1) =>
% 123.15/16.46                                                     (((image1Equiv) =>
% 123.15/16.46                                                       (((image1E) =>
% 123.15/16.46                                                         (((image1I) =>
% 123.15/16.46                                                           (((injFuncInInjFuncSet) =>
% 123.15/16.46                                                             (((injFuncSetFuncIn) =>
% 123.15/16.46                                                               (((injFuncSetFuncInj) =>
% 123.15/16.46                                                                 (((surjFuncSetFuncIn) =>
% 123.15/16.46                                                                   (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2725])).
% 123.15/16.46  thf(zip_derived_cl2749, plain,
% 123.15/16.46      (~ (((eqbreln1) =>
% 123.15/16.46           (((breln1invprop) =>
% 123.15/16.46             (((breln1invI) =>
% 123.15/16.46               (((breln1invE) =>
% 123.15/16.46                 (((breln1compprop) =>
% 123.15/16.46                   (((breln1compI) =>
% 123.15/16.46                     (((breln1compE) =>
% 123.15/16.46                       (((breln1compEex) =>
% 123.15/16.46                         (((breln1unionprop) =>
% 123.15/16.46                           (((breln1unionIL) =>
% 123.15/16.46                             (((breln1unionIR) =>
% 123.15/16.46                               (((breln1unionI) =>
% 123.15/16.46                                 (((breln1unionE) =>
% 123.15/16.46                                   (((breln1unionEcases) =>
% 123.15/16.46                                     (((breln1unionCommutes) =>
% 123.15/16.46                                       (((woz2Ex) =>
% 123.15/16.46                                         (((woz2W) =>
% 123.15/16.46                                           (((woz2A) =>
% 123.15/16.46                                             (((woz2B) =>
% 123.15/16.46                                               (((image1Ex) =>
% 123.15/16.46                                                 (((image1Ex1) =>
% 123.15/16.46                                                   (((image1Equiv) =>
% 123.15/16.46                                                     (((image1E) =>
% 123.15/16.46                                                       (((image1I) =>
% 123.15/16.46                                                         (((injFuncInInjFuncSet) =>
% 123.15/16.46                                                           (((injFuncSetFuncIn) =>
% 123.15/16.46                                                             (((injFuncSetFuncInj) =>
% 123.15/16.46                                                               (((surjFuncSetFuncIn) =>
% 123.15/16.46                                                                 (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                   (((leftInvIsSurj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2736])).
% 123.15/16.46  thf(zip_derived_cl2758, plain,
% 123.15/16.46      (~ (((breln1invprop) =>
% 123.15/16.46           (((breln1invI) =>
% 123.15/16.46             (((breln1invE) =>
% 123.15/16.46               (((breln1compprop) =>
% 123.15/16.46                 (((breln1compI) =>
% 123.15/16.46                   (((breln1compE) =>
% 123.15/16.46                     (((breln1compEex) =>
% 123.15/16.46                       (((breln1unionprop) =>
% 123.15/16.46                         (((breln1unionIL) =>
% 123.15/16.46                           (((breln1unionIR) =>
% 123.15/16.46                             (((breln1unionI) =>
% 123.15/16.46                               (((breln1unionE) =>
% 123.15/16.46                                 (((breln1unionEcases) =>
% 123.15/16.46                                   (((breln1unionCommutes) =>
% 123.15/16.46                                     (((woz2Ex) =>
% 123.15/16.46                                       (((woz2W) =>
% 123.15/16.46                                         (((woz2A) =>
% 123.15/16.46                                           (((woz2B) =>
% 123.15/16.46                                             (((image1Ex) =>
% 123.15/16.46                                               (((image1Ex1) =>
% 123.15/16.46                                                 (((image1Equiv) =>
% 123.15/16.46                                                   (((image1E) =>
% 123.15/16.46                                                     (((image1I) =>
% 123.15/16.46                                                       (((injFuncInInjFuncSet) =>
% 123.15/16.46                                                         (((injFuncSetFuncIn) =>
% 123.15/16.46                                                           (((injFuncSetFuncInj) =>
% 123.15/16.46                                                             (((surjFuncSetFuncIn) =>
% 123.15/16.46                                                               (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                                                 (((leftInvIsSurj) =>
% 123.15/16.46                                                                   (((surjCantorThm) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2749])).
% 123.15/16.46  thf(zip_derived_cl2766, plain,
% 123.15/16.46      (~ (((breln1invI) =>
% 123.15/16.46           (((breln1invE) =>
% 123.15/16.46             (((breln1compprop) =>
% 123.15/16.46               (((breln1compI) =>
% 123.15/16.46                 (((breln1compE) =>
% 123.15/16.46                   (((breln1compEex) =>
% 123.15/16.46                     (((breln1unionprop) =>
% 123.15/16.46                       (((breln1unionIL) =>
% 123.15/16.46                         (((breln1unionIR) =>
% 123.15/16.46                           (((breln1unionI) =>
% 123.15/16.46                             (((breln1unionE) =>
% 123.15/16.46                               (((breln1unionEcases) =>
% 123.15/16.46                                 (((breln1unionCommutes) =>
% 123.15/16.46                                   (((woz2Ex) =>
% 123.15/16.46                                     (((woz2W) =>
% 123.15/16.46                                       (((woz2A) =>
% 123.15/16.46                                         (((woz2B) =>
% 123.15/16.46                                           (((image1Ex) =>
% 123.15/16.46                                             (((image1Ex1) =>
% 123.15/16.46                                               (((image1Equiv) =>
% 123.15/16.46                                                 (((image1E) =>
% 123.15/16.46                                                   (((image1I) =>
% 123.15/16.46                                                     (((injFuncInInjFuncSet) =>
% 123.15/16.46                                                       (((injFuncSetFuncIn) =>
% 123.15/16.46                                                         (((injFuncSetFuncInj) =>
% 123.15/16.46                                                           (((surjFuncSetFuncIn) =>
% 123.15/16.46                                                             (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                                               (((leftInvIsSurj) =>
% 123.15/16.46                                                                 (((surjCantorThm) =>
% 123.15/16.46                                                                   (((foundation2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2758])).
% 123.15/16.46  thf(zip_derived_cl2775, plain,
% 123.15/16.46      (~ (((breln1invE) =>
% 123.15/16.46           (((breln1compprop) =>
% 123.15/16.46             (((breln1compI) =>
% 123.15/16.46               (((breln1compE) =>
% 123.15/16.46                 (((breln1compEex) =>
% 123.15/16.46                   (((breln1unionprop) =>
% 123.15/16.46                     (((breln1unionIL) =>
% 123.15/16.46                       (((breln1unionIR) =>
% 123.15/16.46                         (((breln1unionI) =>
% 123.15/16.46                           (((breln1unionE) =>
% 123.15/16.46                             (((breln1unionEcases) =>
% 123.15/16.46                               (((breln1unionCommutes) =>
% 123.15/16.46                                 (((woz2Ex) =>
% 123.15/16.46                                   (((woz2W) =>
% 123.15/16.46                                     (((woz2A) =>
% 123.15/16.46                                       (((woz2B) =>
% 123.15/16.46                                         (((image1Ex) =>
% 123.15/16.46                                           (((image1Ex1) =>
% 123.15/16.46                                             (((image1Equiv) =>
% 123.15/16.46                                               (((image1E) =>
% 123.15/16.46                                                 (((image1I) =>
% 123.15/16.46                                                   (((injFuncInInjFuncSet) =>
% 123.15/16.46                                                     (((injFuncSetFuncIn) =>
% 123.15/16.46                                                       (((injFuncSetFuncInj) =>
% 123.15/16.46                                                         (((surjFuncSetFuncIn) =>
% 123.15/16.46                                                           (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                                             (((leftInvIsSurj) =>
% 123.15/16.46                                                               (((surjCantorThm) =>
% 123.15/16.46                                                                 (((foundation2) =>
% 123.15/16.46                                                                   (((notinself) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2766])).
% 123.15/16.46  thf(zip_derived_cl2786, plain,
% 123.15/16.46      (~ (((breln1compprop) =>
% 123.15/16.46           (((breln1compI) =>
% 123.15/16.46             (((breln1compE) =>
% 123.15/16.46               (((breln1compEex) =>
% 123.15/16.46                 (((breln1unionprop) =>
% 123.15/16.46                   (((breln1unionIL) =>
% 123.15/16.46                     (((breln1unionIR) =>
% 123.15/16.46                       (((breln1unionI) =>
% 123.15/16.46                         (((breln1unionE) =>
% 123.15/16.46                           (((breln1unionEcases) =>
% 123.15/16.46                             (((breln1unionCommutes) =>
% 123.15/16.46                               (((woz2Ex) =>
% 123.15/16.46                                 (((woz2W) =>
% 123.15/16.46                                   (((woz2A) =>
% 123.15/16.46                                     (((woz2B) =>
% 123.15/16.46                                       (((image1Ex) =>
% 123.15/16.46                                         (((image1Ex1) =>
% 123.15/16.46                                           (((image1Equiv) =>
% 123.15/16.46                                             (((image1E) =>
% 123.15/16.46                                               (((image1I) =>
% 123.15/16.46                                                 (((injFuncInInjFuncSet) =>
% 123.15/16.46                                                   (((injFuncSetFuncIn) =>
% 123.15/16.46                                                     (((injFuncSetFuncInj) =>
% 123.15/16.46                                                       (((surjFuncSetFuncIn) =>
% 123.15/16.46                                                         (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                                           (((leftInvIsSurj) =>
% 123.15/16.46                                                             (((surjCantorThm) =>
% 123.15/16.46                                                               (((foundation2) =>
% 123.15/16.46                                                                 (((notinself) =>
% 123.15/16.46                                                                   (((notinself2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2775])).
% 123.15/16.46  thf(zip_derived_cl2799, plain,
% 123.15/16.46      (~ (((breln1compI) =>
% 123.15/16.46           (((breln1compE) =>
% 123.15/16.46             (((breln1compEex) =>
% 123.15/16.46               (((breln1unionprop) =>
% 123.15/16.46                 (((breln1unionIL) =>
% 123.15/16.46                   (((breln1unionIR) =>
% 123.15/16.46                     (((breln1unionI) =>
% 123.15/16.46                       (((breln1unionE) =>
% 123.15/16.46                         (((breln1unionEcases) =>
% 123.15/16.46                           (((breln1unionCommutes) =>
% 123.15/16.46                             (((woz2Ex) =>
% 123.15/16.46                               (((woz2W) =>
% 123.15/16.46                                 (((woz2A) =>
% 123.15/16.46                                   (((woz2B) =>
% 123.15/16.46                                     (((image1Ex) =>
% 123.15/16.46                                       (((image1Ex1) =>
% 123.15/16.46                                         (((image1Equiv) =>
% 123.15/16.46                                           (((image1E) =>
% 123.15/16.46                                             (((image1I) =>
% 123.15/16.46                                               (((injFuncInInjFuncSet) =>
% 123.15/16.46                                                 (((injFuncSetFuncIn) =>
% 123.15/16.46                                                   (((injFuncSetFuncInj) =>
% 123.15/16.46                                                     (((surjFuncSetFuncIn) =>
% 123.15/16.46                                                       (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                                         (((leftInvIsSurj) =>
% 123.15/16.46                                                           (((surjCantorThm) =>
% 123.15/16.46                                                             (((foundation2) =>
% 123.15/16.46                                                               (((notinself) =>
% 123.15/16.46                                                                 (((notinself2) =>
% 123.15/16.46                                                                   (((omegaSp) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2786])).
% 123.15/16.46  thf(zip_derived_cl2813, plain,
% 123.15/16.46      (~ (((breln1compE) =>
% 123.15/16.46           (((breln1compEex) =>
% 123.15/16.46             (((breln1unionprop) =>
% 123.15/16.46               (((breln1unionIL) =>
% 123.15/16.46                 (((breln1unionIR) =>
% 123.15/16.46                   (((breln1unionI) =>
% 123.15/16.46                     (((breln1unionE) =>
% 123.15/16.46                       (((breln1unionEcases) =>
% 123.15/16.46                         (((breln1unionCommutes) =>
% 123.15/16.46                           (((woz2Ex) =>
% 123.15/16.46                             (((woz2W) =>
% 123.15/16.46                               (((woz2A) =>
% 123.15/16.46                                 (((woz2B) =>
% 123.15/16.46                                   (((image1Ex) =>
% 123.15/16.46                                     (((image1Ex1) =>
% 123.15/16.46                                       (((image1Equiv) =>
% 123.15/16.46                                         (((image1E) =>
% 123.15/16.46                                           (((image1I) =>
% 123.15/16.46                                             (((injFuncInInjFuncSet) =>
% 123.15/16.46                                               (((injFuncSetFuncIn) =>
% 123.15/16.46                                                 (((injFuncSetFuncInj) =>
% 123.15/16.46                                                   (((surjFuncSetFuncIn) =>
% 123.15/16.46                                                     (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                                       (((leftInvIsSurj) =>
% 123.15/16.46                                                         (((surjCantorThm) =>
% 123.15/16.46                                                           (((foundation2) =>
% 123.15/16.46                                                             (((notinself) =>
% 123.15/16.46                                                               (((notinself2) =>
% 123.15/16.46                                                                 (((omegaSp) =>
% 123.15/16.46                                                                   (((omegaSclos) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2799])).
% 123.15/16.46  thf(zip_derived_cl2828, plain,
% 123.15/16.46      (~ (((breln1compEex) =>
% 123.15/16.46           (((breln1unionprop) =>
% 123.15/16.46             (((breln1unionIL) =>
% 123.15/16.46               (((breln1unionIR) =>
% 123.15/16.46                 (((breln1unionI) =>
% 123.15/16.46                   (((breln1unionE) =>
% 123.15/16.46                     (((breln1unionEcases) =>
% 123.15/16.46                       (((breln1unionCommutes) =>
% 123.15/16.46                         (((woz2Ex) =>
% 123.15/16.46                           (((woz2W) =>
% 123.15/16.46                             (((woz2A) =>
% 123.15/16.46                               (((woz2B) =>
% 123.15/16.46                                 (((image1Ex) =>
% 123.15/16.46                                   (((image1Ex1) =>
% 123.15/16.46                                     (((image1Equiv) =>
% 123.15/16.46                                       (((image1E) =>
% 123.15/16.46                                         (((image1I) =>
% 123.15/16.46                                           (((injFuncInInjFuncSet) =>
% 123.15/16.46                                             (((injFuncSetFuncIn) =>
% 123.15/16.46                                               (((injFuncSetFuncInj) =>
% 123.15/16.46                                                 (((surjFuncSetFuncIn) =>
% 123.15/16.46                                                   (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                                     (((leftInvIsSurj) =>
% 123.15/16.46                                                       (((surjCantorThm) =>
% 123.15/16.46                                                         (((foundation2) =>
% 123.15/16.46                                                           (((notinself) =>
% 123.15/16.46                                                             (((notinself2) =>
% 123.15/16.46                                                               (((omegaSp) =>
% 123.15/16.46                                                                 (((omegaSclos) =>
% 123.15/16.46                                                                   (((peano0notS) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2813])).
% 123.15/16.46  thf(zip_derived_cl2843, plain,
% 123.15/16.46      (~ (((breln1unionprop) =>
% 123.15/16.46           (((breln1unionIL) =>
% 123.15/16.46             (((breln1unionIR) =>
% 123.15/16.46               (((breln1unionI) =>
% 123.15/16.46                 (((breln1unionE) =>
% 123.15/16.46                   (((breln1unionEcases) =>
% 123.15/16.46                     (((breln1unionCommutes) =>
% 123.15/16.46                       (((woz2Ex) =>
% 123.15/16.46                         (((woz2W) =>
% 123.15/16.46                           (((woz2A) =>
% 123.15/16.46                             (((woz2B) =>
% 123.15/16.46                               (((image1Ex) =>
% 123.15/16.46                                 (((image1Ex1) =>
% 123.15/16.46                                   (((image1Equiv) =>
% 123.15/16.46                                     (((image1E) =>
% 123.15/16.46                                       (((image1I) =>
% 123.15/16.46                                         (((injFuncInInjFuncSet) =>
% 123.15/16.46                                           (((injFuncSetFuncIn) =>
% 123.15/16.46                                             (((injFuncSetFuncInj) =>
% 123.15/16.46                                               (((surjFuncSetFuncIn) =>
% 123.15/16.46                                                 (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                                   (((leftInvIsSurj) =>
% 123.15/16.46                                                     (((surjCantorThm) =>
% 123.15/16.46                                                       (((foundation2) =>
% 123.15/16.46                                                         (((notinself) =>
% 123.15/16.46                                                           (((notinself2) =>
% 123.15/16.46                                                             (((omegaSp) =>
% 123.15/16.46                                                               (((omegaSclos) =>
% 123.15/16.46                                                                 (((peano0notS) =>
% 123.15/16.46                                                                   (((peanoSinj) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2828])).
% 123.15/16.46  thf(zip_derived_cl2859, plain,
% 123.15/16.46      (~ (((breln1unionIL) =>
% 123.15/16.46           (((breln1unionIR) =>
% 123.15/16.46             (((breln1unionI) =>
% 123.15/16.46               (((breln1unionE) =>
% 123.15/16.46                 (((breln1unionEcases) =>
% 123.15/16.46                   (((breln1unionCommutes) =>
% 123.15/16.46                     (((woz2Ex) =>
% 123.15/16.46                       (((woz2W) =>
% 123.15/16.46                         (((woz2A) =>
% 123.15/16.46                           (((woz2B) =>
% 123.15/16.46                             (((image1Ex) =>
% 123.15/16.46                               (((image1Ex1) =>
% 123.15/16.46                                 (((image1Equiv) =>
% 123.15/16.46                                   (((image1E) =>
% 123.15/16.46                                     (((image1I) =>
% 123.15/16.46                                       (((injFuncInInjFuncSet) =>
% 123.15/16.46                                         (((injFuncSetFuncIn) =>
% 123.15/16.46                                           (((injFuncSetFuncInj) =>
% 123.15/16.46                                             (((surjFuncSetFuncIn) =>
% 123.15/16.46                                               (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                                 (((leftInvIsSurj) =>
% 123.15/16.46                                                   (((surjCantorThm) =>
% 123.15/16.46                                                     (((foundation2) =>
% 123.15/16.46                                                       (((notinself) =>
% 123.15/16.46                                                         (((notinself2) =>
% 123.15/16.46                                                           (((omegaSp) =>
% 123.15/16.46                                                             (((omegaSclos) =>
% 123.15/16.46                                                               (((peano0notS) =>
% 123.15/16.46                                                                 (((peanoSinj) =>
% 123.15/16.46                                                                   (((transitivesetOp1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2843])).
% 123.15/16.46  thf(zip_derived_cl2874, plain,
% 123.15/16.46      (~ (((breln1unionIR) =>
% 123.15/16.46           (((breln1unionI) =>
% 123.15/16.46             (((breln1unionE) =>
% 123.15/16.46               (((breln1unionEcases) =>
% 123.15/16.46                 (((breln1unionCommutes) =>
% 123.15/16.46                   (((woz2Ex) =>
% 123.15/16.46                     (((woz2W) =>
% 123.15/16.46                       (((woz2A) =>
% 123.15/16.46                         (((woz2B) =>
% 123.15/16.46                           (((image1Ex) =>
% 123.15/16.46                             (((image1Ex1) =>
% 123.15/16.46                               (((image1Equiv) =>
% 123.15/16.46                                 (((image1E) =>
% 123.15/16.46                                   (((image1I) =>
% 123.15/16.46                                     (((injFuncInInjFuncSet) =>
% 123.15/16.46                                       (((injFuncSetFuncIn) =>
% 123.15/16.46                                         (((injFuncSetFuncInj) =>
% 123.15/16.46                                           (((surjFuncSetFuncIn) =>
% 123.15/16.46                                             (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                               (((leftInvIsSurj) =>
% 123.15/16.46                                                 (((surjCantorThm) =>
% 123.15/16.46                                                   (((foundation2) =>
% 123.15/16.46                                                     (((notinself) =>
% 123.15/16.46                                                       (((notinself2) =>
% 123.15/16.46                                                         (((omegaSp) =>
% 123.15/16.46                                                           (((omegaSclos) =>
% 123.15/16.46                                                             (((peano0notS) =>
% 123.15/16.46                                                               (((peanoSinj) =>
% 123.15/16.46                                                                 (((transitivesetOp1) =>
% 123.15/16.46                                                                   (((binintTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2859])).
% 123.15/16.46  thf(zip_derived_cl2891, plain,
% 123.15/16.46      (~ (((breln1unionI) =>
% 123.15/16.46           (((breln1unionE) =>
% 123.15/16.46             (((breln1unionEcases) =>
% 123.15/16.46               (((breln1unionCommutes) =>
% 123.15/16.46                 (((woz2Ex) =>
% 123.15/16.46                   (((woz2W) =>
% 123.15/16.46                     (((woz2A) =>
% 123.15/16.46                       (((woz2B) =>
% 123.15/16.46                         (((image1Ex) =>
% 123.15/16.46                           (((image1Ex1) =>
% 123.15/16.46                             (((image1Equiv) =>
% 123.15/16.46                               (((image1E) =>
% 123.15/16.46                                 (((image1I) =>
% 123.15/16.46                                   (((injFuncInInjFuncSet) =>
% 123.15/16.46                                     (((injFuncSetFuncIn) =>
% 123.15/16.46                                       (((injFuncSetFuncInj) =>
% 123.15/16.46                                         (((surjFuncSetFuncIn) =>
% 123.15/16.46                                           (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                             (((leftInvIsSurj) =>
% 123.15/16.46                                               (((surjCantorThm) =>
% 123.15/16.46                                                 (((foundation2) =>
% 123.15/16.46                                                   (((notinself) =>
% 123.15/16.46                                                     (((notinself2) =>
% 123.15/16.46                                                       (((omegaSp) =>
% 123.15/16.46                                                         (((omegaSclos) =>
% 123.15/16.46                                                           (((peano0notS) =>
% 123.15/16.46                                                             (((peanoSinj) =>
% 123.15/16.46                                                               (((transitivesetOp1) =>
% 123.15/16.46                                                                 (((binintTransitive) =>
% 123.15/16.46                                                                   (((transitivesetOp2) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2874])).
% 123.15/16.46  thf(zip_derived_cl2906, plain,
% 123.15/16.46      (~ (((breln1unionE) =>
% 123.15/16.46           (((breln1unionEcases) =>
% 123.15/16.46             (((breln1unionCommutes) =>
% 123.15/16.46               (((woz2Ex) =>
% 123.15/16.46                 (((woz2W) =>
% 123.15/16.46                   (((woz2A) =>
% 123.15/16.46                     (((woz2B) =>
% 123.15/16.46                       (((image1Ex) =>
% 123.15/16.46                         (((image1Ex1) =>
% 123.15/16.46                           (((image1Equiv) =>
% 123.15/16.46                             (((image1E) =>
% 123.15/16.46                               (((image1I) =>
% 123.15/16.46                                 (((injFuncInInjFuncSet) =>
% 123.15/16.46                                   (((injFuncSetFuncIn) =>
% 123.15/16.46                                     (((injFuncSetFuncInj) =>
% 123.15/16.46                                       (((surjFuncSetFuncIn) =>
% 123.15/16.46                                         (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                           (((leftInvIsSurj) =>
% 123.15/16.46                                             (((surjCantorThm) =>
% 123.15/16.46                                               (((foundation2) =>
% 123.15/16.46                                                 (((notinself) =>
% 123.15/16.46                                                   (((notinself2) =>
% 123.15/16.46                                                     (((omegaSp) =>
% 123.15/16.46                                                       (((omegaSclos) =>
% 123.15/16.46                                                         (((peano0notS) =>
% 123.15/16.46                                                           (((peanoSinj) =>
% 123.15/16.46                                                             (((transitivesetOp1) =>
% 123.15/16.46                                                               (((binintTransitive) =>
% 123.15/16.46                                                                 (((transitivesetOp2) =>
% 123.15/16.46                                                                   (((setunionTransitive) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2891])).
% 123.15/16.46  thf(zip_derived_cl2918, plain,
% 123.15/16.46      (~ (((breln1unionEcases) =>
% 123.15/16.46           (((breln1unionCommutes) =>
% 123.15/16.46             (((woz2Ex) =>
% 123.15/16.46               (((woz2W) =>
% 123.15/16.46                 (((woz2A) =>
% 123.15/16.46                   (((woz2B) =>
% 123.15/16.46                     (((image1Ex) =>
% 123.15/16.46                       (((image1Ex1) =>
% 123.15/16.46                         (((image1Equiv) =>
% 123.15/16.46                           (((image1E) =>
% 123.15/16.46                             (((image1I) =>
% 123.15/16.46                               (((injFuncInInjFuncSet) =>
% 123.15/16.46                                 (((injFuncSetFuncIn) =>
% 123.15/16.46                                   (((injFuncSetFuncInj) =>
% 123.15/16.46                                     (((surjFuncSetFuncIn) =>
% 123.15/16.46                                       (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                         (((leftInvIsSurj) =>
% 123.15/16.46                                           (((surjCantorThm) =>
% 123.15/16.46                                             (((foundation2) =>
% 123.15/16.46                                               (((notinself) =>
% 123.15/16.46                                                 (((notinself2) =>
% 123.15/16.46                                                   (((omegaSp) =>
% 123.15/16.46                                                     (((omegaSclos) =>
% 123.15/16.46                                                       (((peano0notS) =>
% 123.15/16.46                                                         (((peanoSinj) =>
% 123.15/16.46                                                           (((transitivesetOp1) =>
% 123.15/16.46                                                             (((binintTransitive) =>
% 123.15/16.46                                                               (((transitivesetOp2) =>
% 123.15/16.46                                                                 (((setunionTransitive) =>
% 123.15/16.46                                                                   (((ordinalMinLem1) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2906])).
% 123.15/16.46  thf(zip_derived_cl2930, plain,
% 123.15/16.46      (~ (((breln1unionCommutes) =>
% 123.15/16.46           (((woz2Ex) =>
% 123.15/16.46             (((woz2W) =>
% 123.15/16.46               (((woz2A) =>
% 123.15/16.46                 (((woz2B) =>
% 123.15/16.46                   (((image1Ex) =>
% 123.15/16.46                     (((image1Ex1) =>
% 123.15/16.46                       (((image1Equiv) =>
% 123.15/16.46                         (((image1E) =>
% 123.15/16.46                           (((image1I) =>
% 123.15/16.46                             (((injFuncInInjFuncSet) =>
% 123.15/16.46                               (((injFuncSetFuncIn) =>
% 123.15/16.46                                 (((injFuncSetFuncInj) =>
% 123.15/16.46                                   (((surjFuncSetFuncIn) =>
% 123.15/16.46                                     (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                       (((leftInvIsSurj) =>
% 123.15/16.46                                         (((surjCantorThm) =>
% 123.15/16.46                                           (((foundation2) =>
% 123.15/16.46                                             (((notinself) =>
% 123.15/16.46                                               (((notinself2) =>
% 123.15/16.46                                                 (((omegaSp) =>
% 123.15/16.46                                                   (((omegaSclos) =>
% 123.15/16.46                                                     (((peano0notS) =>
% 123.15/16.46                                                       (((peanoSinj) =>
% 123.15/16.46                                                         (((transitivesetOp1) =>
% 123.15/16.46                                                           (((binintTransitive) =>
% 123.15/16.46                                                             (((transitivesetOp2) =>
% 123.15/16.46                                                               (((setunionTransitive) =>
% 123.15/16.46                                                                 (((ordinalMinLem1) =>
% 123.15/16.46                                                                   (((!!) @ (
% 123.15/16.46                                                                     ^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2918])).
% 123.15/16.46  thf(zip_derived_cl2941, plain,
% 123.15/16.46      (~ (((woz2Ex) =>
% 123.15/16.46           (((woz2W) =>
% 123.15/16.46             (((woz2A) =>
% 123.15/16.46               (((woz2B) =>
% 123.15/16.46                 (((image1Ex) =>
% 123.15/16.46                   (((image1Ex1) =>
% 123.15/16.46                     (((image1Equiv) =>
% 123.15/16.46                       (((image1E) =>
% 123.15/16.46                         (((image1I) =>
% 123.15/16.46                           (((injFuncInInjFuncSet) =>
% 123.15/16.46                             (((injFuncSetFuncIn) =>
% 123.15/16.46                               (((injFuncSetFuncInj) =>
% 123.15/16.46                                 (((surjFuncSetFuncIn) =>
% 123.15/16.46                                   (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                     (((leftInvIsSurj) =>
% 123.15/16.46                                       (((surjCantorThm) =>
% 123.15/16.46                                         (((foundation2) =>
% 123.15/16.46                                           (((notinself) =>
% 123.15/16.46                                             (((notinself2) =>
% 123.15/16.46                                               (((omegaSp) =>
% 123.15/16.46                                                 (((omegaSclos) =>
% 123.15/16.46                                                   (((peano0notS) =>
% 123.15/16.46                                                     (((peanoSinj) =>
% 123.15/16.46                                                       (((transitivesetOp1) =>
% 123.15/16.46                                                         (((binintTransitive) =>
% 123.15/16.46                                                           (((transitivesetOp2) =>
% 123.15/16.46                                                             (((setunionTransitive) =>
% 123.15/16.46                                                               (((ordinalMinLem1) =>
% 123.15/16.46                                                                 (((!!) @ (
% 123.15/16.46                                                                   ^[Y0 : $i]:
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2930])).
% 123.15/16.46  thf(zip_derived_cl2952, plain,
% 123.15/16.46      (~ (((woz2W) =>
% 123.15/16.46           (((woz2A) =>
% 123.15/16.46             (((woz2B) =>
% 123.15/16.46               (((image1Ex) =>
% 123.15/16.46                 (((image1Ex1) =>
% 123.15/16.46                   (((image1Equiv) =>
% 123.15/16.46                     (((image1E) =>
% 123.15/16.46                       (((image1I) =>
% 123.15/16.46                         (((injFuncInInjFuncSet) =>
% 123.15/16.46                           (((injFuncSetFuncIn) =>
% 123.15/16.46                             (((injFuncSetFuncInj) =>
% 123.15/16.46                               (((surjFuncSetFuncIn) =>
% 123.15/16.46                                 (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                   (((leftInvIsSurj) =>
% 123.15/16.46                                     (((surjCantorThm) =>
% 123.15/16.46                                       (((foundation2) =>
% 123.15/16.46                                         (((notinself) =>
% 123.15/16.46                                           (((notinself2) =>
% 123.15/16.46                                             (((omegaSp) =>
% 123.15/16.46                                               (((omegaSclos) =>
% 123.15/16.46                                                 (((peano0notS) =>
% 123.15/16.46                                                   (((peanoSinj) =>
% 123.15/16.46                                                     (((transitivesetOp1) =>
% 123.15/16.46                                                       (((binintTransitive) =>
% 123.15/16.46                                                         (((transitivesetOp2) =>
% 123.15/16.46                                                           (((setunionTransitive) =>
% 123.15/16.46                                                             (((ordinalMinLem1) =>
% 123.15/16.46                                                               (((!!) @ (
% 123.15/16.46                                                                 ^[Y0 : $i]:
% 123.15/16.46                                                                   (((ordinal @ 
% 123.15/16.46                                                                     Y0) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2941])).
% 123.15/16.46  thf(zip_derived_cl2964, plain,
% 123.15/16.46      (~ (((woz2A) =>
% 123.15/16.46           (((woz2B) =>
% 123.15/16.46             (((image1Ex) =>
% 123.15/16.46               (((image1Ex1) =>
% 123.15/16.46                 (((image1Equiv) =>
% 123.15/16.46                   (((image1E) =>
% 123.15/16.46                     (((image1I) =>
% 123.15/16.46                       (((injFuncInInjFuncSet) =>
% 123.15/16.46                         (((injFuncSetFuncIn) =>
% 123.15/16.46                           (((injFuncSetFuncInj) =>
% 123.15/16.46                             (((surjFuncSetFuncIn) =>
% 123.15/16.46                               (((surjFuncSetFuncSurj) =>
% 123.15/16.46                                 (((leftInvIsSurj) =>
% 123.15/16.46                                   (((surjCantorThm) =>
% 123.15/16.46                                     (((foundation2) =>
% 123.15/16.46                                       (((notinself) =>
% 123.15/16.46                                         (((notinself2) =>
% 123.15/16.46                                           (((omegaSp) =>
% 123.15/16.46                                             (((omegaSclos) =>
% 123.15/16.46                                               (((peano0notS) =>
% 123.15/16.46                                                 (((peanoSinj) =>
% 123.15/16.46                                                   (((transitivesetOp1) =>
% 123.15/16.46                                                     (((binintTransitive) =>
% 123.15/16.46                                                       (((transitivesetOp2) =>
% 123.15/16.46                                                         (((setunionTransitive) =>
% 123.15/16.46                                                           (((ordinalMinLem1) =>
% 123.15/16.46                                                             (((!!) @ (
% 123.15/16.46                                                               ^[Y0 : $i]:
% 123.15/16.46                                                                 (((ordinal @ 
% 123.15/16.46                                                                   Y0) =>
% 123.15/16.46                                                                   (((!!) @ (
% 123.15/16.46                                                                     ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2952])).
% 123.15/16.46  thf(zip_derived_cl2977, plain,
% 123.15/16.46      (~ (((woz2B) =>
% 123.15/16.46           (((image1Ex) =>
% 123.15/16.46             (((image1Ex1) =>
% 123.15/16.46               (((image1Equiv) =>
% 123.15/16.46                 (((image1E) =>
% 123.15/16.46                   (((image1I) =>
% 123.15/16.46                     (((injFuncInInjFuncSet) =>
% 123.15/16.46                       (((injFuncSetFuncIn) =>
% 123.15/16.46                         (((injFuncSetFuncInj) =>
% 123.15/16.46                           (((surjFuncSetFuncIn) =>
% 123.15/16.46                             (((surjFuncSetFuncSurj) =>
% 123.15/16.46                               (((leftInvIsSurj) =>
% 123.15/16.46                                 (((surjCantorThm) =>
% 123.15/16.46                                   (((foundation2) =>
% 123.15/16.46                                     (((notinself) =>
% 123.15/16.46                                       (((notinself2) =>
% 123.15/16.46                                         (((omegaSp) =>
% 123.15/16.46                                           (((omegaSclos) =>
% 123.15/16.46                                             (((peano0notS) =>
% 123.15/16.46                                               (((peanoSinj) =>
% 123.15/16.46                                                 (((transitivesetOp1) =>
% 123.15/16.46                                                   (((binintTransitive) =>
% 123.15/16.46                                                     (((transitivesetOp2) =>
% 123.15/16.46                                                       (((setunionTransitive) =>
% 123.15/16.46                                                         (((ordinalMinLem1) =>
% 123.15/16.46                                                           (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2964])).
% 123.15/16.46  thf(zip_derived_cl2991, plain,
% 123.15/16.46      (~ (((image1Ex) =>
% 123.15/16.46           (((image1Ex1) =>
% 123.15/16.46             (((image1Equiv) =>
% 123.15/16.46               (((image1E) =>
% 123.15/16.46                 (((image1I) =>
% 123.15/16.46                   (((injFuncInInjFuncSet) =>
% 123.15/16.46                     (((injFuncSetFuncIn) =>
% 123.15/16.46                       (((injFuncSetFuncInj) =>
% 123.15/16.46                         (((surjFuncSetFuncIn) =>
% 123.15/16.46                           (((surjFuncSetFuncSurj) =>
% 123.15/16.46                             (((leftInvIsSurj) =>
% 123.15/16.46                               (((surjCantorThm) =>
% 123.15/16.46                                 (((foundation2) =>
% 123.15/16.46                                   (((notinself) =>
% 123.15/16.46                                     (((notinself2) =>
% 123.15/16.46                                       (((omegaSp) =>
% 123.15/16.46                                         (((omegaSclos) =>
% 123.15/16.46                                           (((peano0notS) =>
% 123.15/16.46                                             (((peanoSinj) =>
% 123.15/16.46                                               (((transitivesetOp1) =>
% 123.15/16.46                                                 (((binintTransitive) =>
% 123.15/16.46                                                   (((transitivesetOp2) =>
% 123.15/16.46                                                     (((setunionTransitive) =>
% 123.15/16.46                                                       (((ordinalMinLem1) =>
% 123.15/16.46                                                         (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                      (ordinal @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2977])).
% 123.15/16.46  thf(zip_derived_cl3008, plain,
% 123.15/16.46      (~ (((image1Ex1) =>
% 123.15/16.46           (((image1Equiv) =>
% 123.15/16.46             (((image1E) =>
% 123.15/16.46               (((image1I) =>
% 123.15/16.46                 (((injFuncInInjFuncSet) =>
% 123.15/16.46                   (((injFuncSetFuncIn) =>
% 123.15/16.46                     (((injFuncSetFuncInj) =>
% 123.15/16.46                       (((surjFuncSetFuncIn) =>
% 123.15/16.46                         (((surjFuncSetFuncSurj) =>
% 123.15/16.46                           (((leftInvIsSurj) =>
% 123.15/16.46                             (((surjCantorThm) =>
% 123.15/16.46                               (((foundation2) =>
% 123.15/16.46                                 (((notinself) =>
% 123.15/16.46                                   (((notinself2) =>
% 123.15/16.46                                     (((omegaSp) =>
% 123.15/16.46                                       (((omegaSclos) =>
% 123.15/16.46                                         (((peano0notS) =>
% 123.15/16.46                                           (((peanoSinj) =>
% 123.15/16.46                                             (((transitivesetOp1) =>
% 123.15/16.46                                               (((binintTransitive) =>
% 123.15/16.46                                                 (((transitivesetOp2) =>
% 123.15/16.46                                                   (((setunionTransitive) =>
% 123.15/16.46                                                     (((ordinalMinLem1) =>
% 123.15/16.46                                                       (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                                                   (((ordinal @ 
% 123.15/16.46                                                                     Y0) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (!!) @ (
% 123.15/16.46                                                                     ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2991])).
% 123.15/16.46  thf(zip_derived_cl3022, plain,
% 123.15/16.46      (~ (((image1Equiv) =>
% 123.15/16.46           (((image1E) =>
% 123.15/16.46             (((image1I) =>
% 123.15/16.46               (((injFuncInInjFuncSet) =>
% 123.15/16.46                 (((injFuncSetFuncIn) =>
% 123.15/16.46                   (((injFuncSetFuncInj) =>
% 123.15/16.46                     (((surjFuncSetFuncIn) =>
% 123.15/16.46                       (((surjFuncSetFuncSurj) =>
% 123.15/16.46                         (((leftInvIsSurj) =>
% 123.15/16.46                           (((surjCantorThm) =>
% 123.15/16.46                             (((foundation2) =>
% 123.15/16.46                               (((notinself) =>
% 123.15/16.46                                 (((notinself2) =>
% 123.15/16.46                                   (((omegaSp) =>
% 123.15/16.46                                     (((omegaSclos) =>
% 123.15/16.46                                       (((peano0notS) =>
% 123.15/16.46                                         (((peanoSinj) =>
% 123.15/16.46                                           (((transitivesetOp1) =>
% 123.15/16.46                                             (((binintTransitive) =>
% 123.15/16.46                                               (((transitivesetOp2) =>
% 123.15/16.46                                                 (((setunionTransitive) =>
% 123.15/16.46                                                   (((ordinalMinLem1) =>
% 123.15/16.46                                                     (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                                                 (((ordinal @ 
% 123.15/16.46                                                                   Y0) =>
% 123.15/16.46                                                                   (((!!) @ (
% 123.15/16.46                                                                     ^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3008])).
% 123.15/16.46  thf(zip_derived_cl3035, plain,
% 123.15/16.46      (~ (((image1E) =>
% 123.15/16.46           (((image1I) =>
% 123.15/16.46             (((injFuncInInjFuncSet) =>
% 123.15/16.46               (((injFuncSetFuncIn) =>
% 123.15/16.46                 (((injFuncSetFuncInj) =>
% 123.15/16.46                   (((surjFuncSetFuncIn) =>
% 123.15/16.46                     (((surjFuncSetFuncSurj) =>
% 123.15/16.46                       (((leftInvIsSurj) =>
% 123.15/16.46                         (((surjCantorThm) =>
% 123.15/16.46                           (((foundation2) =>
% 123.15/16.46                             (((notinself) =>
% 123.15/16.46                               (((notinself2) =>
% 123.15/16.46                                 (((omegaSp) =>
% 123.15/16.46                                   (((omegaSclos) =>
% 123.15/16.46                                     (((peano0notS) =>
% 123.15/16.46                                       (((peanoSinj) =>
% 123.15/16.46                                         (((transitivesetOp1) =>
% 123.15/16.46                                           (((binintTransitive) =>
% 123.15/16.46                                             (((transitivesetOp2) =>
% 123.15/16.46                                               (((setunionTransitive) =>
% 123.15/16.46                                                 (((ordinalMinLem1) =>
% 123.15/16.46                                                   (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                                               (((ordinal @ 
% 123.15/16.46                                                                 Y0) =>
% 123.15/16.46                                                                 (((!!) @ (
% 123.15/16.46                                                                   ^[Y1 : $i]:
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3022])).
% 123.15/16.46  thf(zip_derived_cl3048, plain,
% 123.15/16.46      (~ (((image1I) =>
% 123.15/16.46           (((injFuncInInjFuncSet) =>
% 123.15/16.46             (((injFuncSetFuncIn) =>
% 123.15/16.46               (((injFuncSetFuncInj) =>
% 123.15/16.46                 (((surjFuncSetFuncIn) =>
% 123.15/16.46                   (((surjFuncSetFuncSurj) =>
% 123.15/16.46                     (((leftInvIsSurj) =>
% 123.15/16.46                       (((surjCantorThm) =>
% 123.15/16.46                         (((foundation2) =>
% 123.15/16.46                           (((notinself) =>
% 123.15/16.46                             (((notinself2) =>
% 123.15/16.46                               (((omegaSp) =>
% 123.15/16.46                                 (((omegaSclos) =>
% 123.15/16.46                                   (((peano0notS) =>
% 123.15/16.46                                     (((peanoSinj) =>
% 123.15/16.46                                       (((transitivesetOp1) =>
% 123.15/16.46                                         (((binintTransitive) =>
% 123.15/16.46                                           (((transitivesetOp2) =>
% 123.15/16.46                                             (((setunionTransitive) =>
% 123.15/16.46                                               (((ordinalMinLem1) =>
% 123.15/16.46                                                 (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                                             (((ordinal @ 
% 123.15/16.46                                                               Y0) =>
% 123.15/16.46                                                               (((!!) @ (
% 123.15/16.46                                                                 ^[Y1 : $i]:
% 123.15/16.46                                                                   (((!!) @ (
% 123.15/16.46                                                                     ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3035])).
% 123.15/16.46  thf(zip_derived_cl3064, plain,
% 123.15/16.46      (~ (((injFuncInInjFuncSet) =>
% 123.15/16.46           (((injFuncSetFuncIn) =>
% 123.15/16.46             (((injFuncSetFuncInj) =>
% 123.15/16.46               (((surjFuncSetFuncIn) =>
% 123.15/16.46                 (((surjFuncSetFuncSurj) =>
% 123.15/16.46                   (((leftInvIsSurj) =>
% 123.15/16.46                     (((surjCantorThm) =>
% 123.15/16.46                       (((foundation2) =>
% 123.15/16.46                         (((notinself) =>
% 123.15/16.46                           (((notinself2) =>
% 123.15/16.46                             (((omegaSp) =>
% 123.15/16.46                               (((omegaSclos) =>
% 123.15/16.46                                 (((peano0notS) =>
% 123.15/16.46                                   (((peanoSinj) =>
% 123.15/16.46                                     (((transitivesetOp1) =>
% 123.15/16.46                                       (((binintTransitive) =>
% 123.15/16.46                                         (((transitivesetOp2) =>
% 123.15/16.46                                           (((setunionTransitive) =>
% 123.15/16.46                                             (((ordinalMinLem1) =>
% 123.15/16.46                                               (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                                           (((ordinal @ Y0) =>
% 123.15/16.46                                                             (((!!) @ (
% 123.15/16.46                                                               ^[Y1 : $i]:
% 123.15/16.46                                                                 (((!!) @ (
% 123.15/16.46                                                                   ^[Y2 : $i]:
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3048])).
% 123.15/16.46  thf(zip_derived_cl3078, plain,
% 123.15/16.46      (~ (((injFuncSetFuncIn) =>
% 123.15/16.46           (((injFuncSetFuncInj) =>
% 123.15/16.46             (((surjFuncSetFuncIn) =>
% 123.15/16.46               (((surjFuncSetFuncSurj) =>
% 123.15/16.46                 (((leftInvIsSurj) =>
% 123.15/16.46                   (((surjCantorThm) =>
% 123.15/16.46                     (((foundation2) =>
% 123.15/16.46                       (((notinself) =>
% 123.15/16.46                         (((notinself2) =>
% 123.15/16.46                           (((omegaSp) =>
% 123.15/16.46                             (((omegaSclos) =>
% 123.15/16.46                               (((peano0notS) =>
% 123.15/16.46                                 (((peanoSinj) =>
% 123.15/16.46                                   (((transitivesetOp1) =>
% 123.15/16.46                                     (((binintTransitive) =>
% 123.15/16.46                                       (((transitivesetOp2) =>
% 123.15/16.46                                         (((setunionTransitive) =>
% 123.15/16.46                                           (((ordinalMinLem1) =>
% 123.15/16.46                                             (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                                         (((ordinal @ Y0) =>
% 123.15/16.46                                                           (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3064])).
% 123.15/16.46  thf(zip_derived_cl3091, plain,
% 123.15/16.46      (~ (((injFuncSetFuncInj) =>
% 123.15/16.46           (((surjFuncSetFuncIn) =>
% 123.15/16.46             (((surjFuncSetFuncSurj) =>
% 123.15/16.46               (((leftInvIsSurj) =>
% 123.15/16.46                 (((surjCantorThm) =>
% 123.15/16.46                   (((foundation2) =>
% 123.15/16.46                     (((notinself) =>
% 123.15/16.46                       (((notinself2) =>
% 123.15/16.46                         (((omegaSp) =>
% 123.15/16.46                           (((omegaSclos) =>
% 123.15/16.46                             (((peano0notS) =>
% 123.15/16.46                               (((peanoSinj) =>
% 123.15/16.46                                 (((transitivesetOp1) =>
% 123.15/16.46                                   (((binintTransitive) =>
% 123.15/16.46                                     (((transitivesetOp2) =>
% 123.15/16.46                                       (((setunionTransitive) =>
% 123.15/16.46                                         (((ordinalMinLem1) =>
% 123.15/16.46                                           (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                                       (((ordinal @ Y0) =>
% 123.15/16.46                                                         (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3078])).
% 123.15/16.46  thf(zip_derived_cl3103, plain,
% 123.15/16.46      (~ (((surjFuncSetFuncIn) =>
% 123.15/16.46           (((surjFuncSetFuncSurj) =>
% 123.15/16.46             (((leftInvIsSurj) =>
% 123.15/16.46               (((surjCantorThm) =>
% 123.15/16.46                 (((foundation2) =>
% 123.15/16.46                   (((notinself) =>
% 123.15/16.46                     (((notinself2) =>
% 123.15/16.46                       (((omegaSp) =>
% 123.15/16.46                         (((omegaSclos) =>
% 123.15/16.46                           (((peano0notS) =>
% 123.15/16.46                             (((peanoSinj) =>
% 123.15/16.46                               (((transitivesetOp1) =>
% 123.15/16.46                                 (((binintTransitive) =>
% 123.15/16.46                                   (((transitivesetOp2) =>
% 123.15/16.46                                     (((setunionTransitive) =>
% 123.15/16.46                                       (((ordinalMinLem1) =>
% 123.15/16.46                                         (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                                     (((ordinal @ Y0) =>
% 123.15/16.46                                                       (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                                                   (((!!) @ (
% 123.15/16.46                                                                     ^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3091])).
% 123.15/16.46  thf(zip_derived_cl3114, plain,
% 123.15/16.46      (~ (((surjFuncSetFuncSurj) =>
% 123.15/16.46           (((leftInvIsSurj) =>
% 123.15/16.46             (((surjCantorThm) =>
% 123.15/16.46               (((foundation2) =>
% 123.15/16.46                 (((notinself) =>
% 123.15/16.46                   (((notinself2) =>
% 123.15/16.46                     (((omegaSp) =>
% 123.15/16.46                       (((omegaSclos) =>
% 123.15/16.46                         (((peano0notS) =>
% 123.15/16.46                           (((peanoSinj) =>
% 123.15/16.46                             (((transitivesetOp1) =>
% 123.15/16.46                               (((binintTransitive) =>
% 123.15/16.46                                 (((transitivesetOp2) =>
% 123.15/16.46                                   (((setunionTransitive) =>
% 123.15/16.46                                     (((ordinalMinLem1) =>
% 123.15/16.46                                       (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                                   (((ordinal @ Y0) =>
% 123.15/16.46                                                     (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                                                 (((!!) @ (
% 123.15/16.46                                                                   ^[Y2 : $i]:
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3103])).
% 123.15/16.46  thf(zip_derived_cl3126, plain,
% 123.15/16.46      (~ (((leftInvIsSurj) =>
% 123.15/16.46           (((surjCantorThm) =>
% 123.15/16.46             (((foundation2) =>
% 123.15/16.46               (((notinself) =>
% 123.15/16.46                 (((notinself2) =>
% 123.15/16.46                   (((omegaSp) =>
% 123.15/16.46                     (((omegaSclos) =>
% 123.15/16.46                       (((peano0notS) =>
% 123.15/16.46                         (((peanoSinj) =>
% 123.15/16.46                           (((transitivesetOp1) =>
% 123.15/16.46                             (((binintTransitive) =>
% 123.15/16.46                               (((transitivesetOp2) =>
% 123.15/16.46                                 (((setunionTransitive) =>
% 123.15/16.46                                   (((ordinalMinLem1) =>
% 123.15/16.46                                     (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                                 (((ordinal @ Y0) =>
% 123.15/16.46                                                   (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                                               (((!!) @ (
% 123.15/16.46                                                                 ^[Y2 : $i]:
% 123.15/16.46                                                                   (((in @ 
% 123.15/16.46                                                                     Y2 @ 
% 123.15/16.46                                                                     Y0) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (in @ 
% 123.15/16.46                                                                     Y1 @ 
% 123.15/16.46                                                                     Y2) =>
% 123.15/16.46                                                                     (in @ 
% 123.15/16.46                                                                     Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3114])).
% 123.15/16.46  thf(zip_derived_cl3138, plain,
% 123.15/16.46      (~ (((surjCantorThm) =>
% 123.15/16.46           (((foundation2) =>
% 123.15/16.46             (((notinself) =>
% 123.15/16.46               (((notinself2) =>
% 123.15/16.46                 (((omegaSp) =>
% 123.15/16.46                   (((omegaSclos) =>
% 123.15/16.46                     (((peano0notS) =>
% 123.15/16.46                       (((peanoSinj) =>
% 123.15/16.46                         (((transitivesetOp1) =>
% 123.15/16.46                           (((binintTransitive) =>
% 123.15/16.46                             (((transitivesetOp2) =>
% 123.15/16.46                               (((setunionTransitive) =>
% 123.15/16.46                                 (((ordinalMinLem1) =>
% 123.15/16.46                                   (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                               (((ordinal @ Y0) =>
% 123.15/16.46                                                 (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                                             (((!!) @ (
% 123.15/16.46                                                               ^[Y2 : $i]:
% 123.15/16.46                                                                 (((in @ Y2 @ 
% 123.15/16.46                                                                   Y0) =>
% 123.15/16.46                                                                   (((in @ 
% 123.15/16.46                                                                     Y1 @ 
% 123.15/16.46                                                                     Y2) =>
% 123.15/16.46                                                                     (in @ 
% 123.15/16.46                                                                     Y1 @ Y0))))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3126])).
% 123.15/16.46  thf(zip_derived_cl3148, plain,
% 123.15/16.46      (~ (((foundation2) =>
% 123.15/16.46           (((notinself) =>
% 123.15/16.46             (((notinself2) =>
% 123.15/16.46               (((omegaSp) =>
% 123.15/16.46                 (((omegaSclos) =>
% 123.15/16.46                   (((peano0notS) =>
% 123.15/16.46                     (((peanoSinj) =>
% 123.15/16.46                       (((transitivesetOp1) =>
% 123.15/16.46                         (((binintTransitive) =>
% 123.15/16.46                           (((transitivesetOp2) =>
% 123.15/16.46                             (((setunionTransitive) =>
% 123.15/16.46                               (((ordinalMinLem1) =>
% 123.15/16.46                                 (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                             (((ordinal @ Y0) =>
% 123.15/16.46                                               (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                                           (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3138])).
% 123.15/16.46  thf(zip_derived_cl3157, plain,
% 123.15/16.46      (~ (((notinself) =>
% 123.15/16.46           (((notinself2) =>
% 123.15/16.46             (((omegaSp) =>
% 123.15/16.46               (((omegaSclos) =>
% 123.15/16.46                 (((peano0notS) =>
% 123.15/16.46                   (((peanoSinj) =>
% 123.15/16.46                     (((transitivesetOp1) =>
% 123.15/16.46                       (((binintTransitive) =>
% 123.15/16.46                         (((transitivesetOp2) =>
% 123.15/16.46                           (((setunionTransitive) =>
% 123.15/16.46                             (((ordinalMinLem1) =>
% 123.15/16.46                               (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                           (((ordinal @ Y0) =>
% 123.15/16.46                                             (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                                         (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y1 @ Y0))))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3148])).
% 123.15/16.46  thf(zip_derived_cl3163, plain,
% 123.15/16.46      (~ (((notinself2) =>
% 123.15/16.46           (((omegaSp) =>
% 123.15/16.46             (((omegaSclos) =>
% 123.15/16.46               (((peano0notS) =>
% 123.15/16.46                 (((peanoSinj) =>
% 123.15/16.46                   (((transitivesetOp1) =>
% 123.15/16.46                     (((binintTransitive) =>
% 123.15/16.46                       (((transitivesetOp2) =>
% 123.15/16.46                         (((setunionTransitive) =>
% 123.15/16.46                           (((ordinalMinLem1) =>
% 123.15/16.46                             (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                         (((ordinal @ Y0) =>
% 123.15/16.46                                           (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                                       (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                                   (((in @ 
% 123.15/16.46                                                                     Y2 @ 
% 123.15/16.46                                                                     Y0) =>
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                     (in @ 
% 123.15/16.46                                                                     Y1 @ 
% 123.15/16.46                                                                     Y2) =>
% 123.15/16.46                                                                     (in @ 
% 123.15/16.46                                                                     Y1 @ Y0))))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3157])).
% 123.15/16.46  thf(zip_derived_cl3170, plain,
% 123.15/16.46      (~ (((omegaSp) =>
% 123.15/16.46           (((omegaSclos) =>
% 123.15/16.46             (((peano0notS) =>
% 123.15/16.46               (((peanoSinj) =>
% 123.15/16.46                 (((transitivesetOp1) =>
% 123.15/16.46                   (((binintTransitive) =>
% 123.15/16.46                     (((transitivesetOp2) =>
% 123.15/16.46                       (((setunionTransitive) =>
% 123.15/16.46                         (((ordinalMinLem1) =>
% 123.15/16.46                           (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                       (((ordinal @ Y0) =>
% 123.15/16.46                                         (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                                     (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                                 (((in @ Y2 @ 
% 123.15/16.46                                                                   Y0) =>
% 123.15/16.46                                                                   (((in @ 
% 123.15/16.46                                                                     Y1 @ 
% 123.15/16.46                                                                     Y2) =>
% 123.15/16.46                                                                     (in @ 
% 123.15/16.46                                                                     Y1 @ Y0))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3163])).
% 123.15/16.46  thf(zip_derived_cl3177, plain,
% 123.15/16.46      (~ (((omegaSclos) =>
% 123.15/16.46           (((peano0notS) =>
% 123.15/16.46             (((peanoSinj) =>
% 123.15/16.46               (((transitivesetOp1) =>
% 123.15/16.46                 (((binintTransitive) =>
% 123.15/16.46                   (((transitivesetOp2) =>
% 123.15/16.46                     (((setunionTransitive) =>
% 123.15/16.46                       (((ordinalMinLem1) =>
% 123.15/16.46                         (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                     (((ordinal @ Y0) =>
% 123.15/16.46                                       (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                                   (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                               (((in @ Y2 @ 
% 123.15/16.46                                                                 Y0) =>
% 123.15/16.46                                                                 (((in @ Y1 @ 
% 123.15/16.46                                                                   Y2) =>
% 123.15/16.46                                                                   (in @ Y1 @ 
% 123.15/16.46                                                                   Y0))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3170])).
% 123.15/16.46  thf(zip_derived_cl3185, plain,
% 123.15/16.46      (~ (((peano0notS) =>
% 123.15/16.46           (((peanoSinj) =>
% 123.15/16.46             (((transitivesetOp1) =>
% 123.15/16.46               (((binintTransitive) =>
% 123.15/16.46                 (((transitivesetOp2) =>
% 123.15/16.46                   (((setunionTransitive) =>
% 123.15/16.46                     (((ordinalMinLem1) =>
% 123.15/16.46                       (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                   (((ordinal @ Y0) =>
% 123.15/16.46                                     (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                                 (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                             (((in @ Y2 @ 
% 123.15/16.46                                                               Y0) =>
% 123.15/16.46                                                               (((in @ Y1 @ 
% 123.15/16.46                                                                 Y2) => (in @ 
% 123.15/16.46                                                                 Y1 @ Y0))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3177])).
% 123.15/16.46  thf(zip_derived_cl3196, plain,
% 123.15/16.46      (~ (((peanoSinj) =>
% 123.15/16.46           (((transitivesetOp1) =>
% 123.15/16.46             (((binintTransitive) =>
% 123.15/16.46               (((transitivesetOp2) =>
% 123.15/16.46                 (((setunionTransitive) =>
% 123.15/16.46                   (((ordinalMinLem1) =>
% 123.15/16.46                     (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                                 (((ordinal @ Y0) =>
% 123.15/16.46                                   (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                               (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                           (((in @ Y2 @ Y0) =>
% 123.15/16.46                                                             (((in @ Y1 @ 
% 123.15/16.46                                                               Y2) => (in @ 
% 123.15/16.46                                                               Y1 @ Y0))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3185])).
% 123.15/16.46  thf(zip_derived_cl3205, plain,
% 123.15/16.46      (~ (((transitivesetOp1) =>
% 123.15/16.46           (((binintTransitive) =>
% 123.15/16.46             (((transitivesetOp2) =>
% 123.15/16.46               (((setunionTransitive) =>
% 123.15/16.46                 (((ordinalMinLem1) =>
% 123.15/16.46                   (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                               (((ordinal @ Y0) =>
% 123.15/16.46                                 (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                             (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                         (((in @ Y2 @ Y0) =>
% 123.15/16.46                                                           (((in @ Y1 @ Y2) =>
% 123.15/16.46                                                             (in @ Y1 @ Y0))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3196])).
% 123.15/16.46  thf(zip_derived_cl3211, plain,
% 123.15/16.46      (~ (((binintTransitive) =>
% 123.15/16.46           (((transitivesetOp2) =>
% 123.15/16.46             (((setunionTransitive) =>
% 123.15/16.46               (((ordinalMinLem1) =>
% 123.15/16.46                 (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                             (((ordinal @ Y0) =>
% 123.15/16.46                               (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                           (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                       (((in @ Y2 @ Y0) =>
% 123.15/16.46                                                         (((in @ Y1 @ Y2) =>
% 123.15/16.46                                                           (in @ Y1 @ Y0))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3205])).
% 123.15/16.46  thf(zip_derived_cl3217, plain,
% 123.15/16.46      (~ (((transitivesetOp2) =>
% 123.15/16.46           (((setunionTransitive) =>
% 123.15/16.46             (((ordinalMinLem1) =>
% 123.15/16.46               (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                           (((ordinal @ Y0) =>
% 123.15/16.46                             (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                         (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                     (((in @ Y2 @ Y0) =>
% 123.15/16.46                                                       (((in @ Y1 @ Y2) =>
% 123.15/16.46                                                         (in @ Y1 @ Y0))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3211])).
% 123.15/16.46  thf(zip_derived_cl3225, plain,
% 123.15/16.46      (~ (((setunionTransitive) =>
% 123.15/16.46           (((ordinalMinLem1) =>
% 123.15/16.46             (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                         (((ordinal @ Y0) =>
% 123.15/16.46                           (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                       (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                   (((in @ Y2 @ Y0) =>
% 123.15/16.46                                                     (((in @ Y1 @ Y2) => (in @ 
% 123.15/16.46                                                       Y1 @ Y0))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3217])).
% 123.15/16.46  thf(zip_derived_cl3232, plain,
% 123.15/16.46      (~ (((ordinalMinLem1) =>
% 123.15/16.46           (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                       (((ordinal @ Y0) =>
% 123.15/16.46                         (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                     (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                 (((in @ Y2 @ Y0) =>
% 123.15/16.46                                                   (((in @ Y1 @ Y2) => (in @ 
% 123.15/16.46                                                     Y1 @ Y0))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3225])).
% 123.15/16.46  thf(zip_derived_cl3239, plain,
% 123.15/16.46      (~ (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                     (((ordinal @ Y0) =>
% 123.15/16.46                       (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                   (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                               (((in @ Y2 @ Y0) =>
% 123.15/16.46                                                 (((in @ Y1 @ Y2) => (in @ 
% 123.15/16.46                                                   Y1 @ Y0))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3232])).
% 123.15/16.46  thf(zip_derived_cl3246, plain,
% 123.15/16.46      (~ (((ordinal @ '#sk1597') =>
% 123.15/16.46           (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                       (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                   (((in @ Y1 @ '#sk1597') =>
% 123.15/16.46                                     (((in @ Y0 @ Y1) => (in @ Y0 @ '#sk1597')))))))))))))),
% 123.15/16.46      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3239])).
% 123.15/16.46  thf(zip_derived_cl3257, plain,
% 123.15/16.46      (~ (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                     (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                 (((in @ Y1 @ '#sk1597') =>
% 123.15/16.46                                   (((in @ Y0 @ Y1) => (in @ Y0 @ '#sk1597')))))))))))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3246])).
% 123.15/16.46  thf(zip_derived_cl3269, plain,
% 123.15/16.46      (~ (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                     (((in @ Y0 @ '#sk1597') =>
% 123.15/16.46                       (((in @ '#sk1599' @ Y0) => (in @ '#sk1599' @ '#sk1597'))))))))),
% 123.15/16.46      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3257])).
% 123.15/16.46  thf(zip_derived_cl3277, plain,
% 123.15/16.46      (~ (((in @ '#sk1600' @ '#sk1597') =>
% 123.15/16.46           (((in @ '#sk1599' @ '#sk1600') => (in @ '#sk1599' @ '#sk1597')))))),
% 123.15/16.46      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3269])).
% 123.15/16.46  thf(zip_derived_cl3285, plain,
% 123.15/16.46      (~ (((in @ '#sk1599' @ '#sk1600') => (in @ '#sk1599' @ '#sk1597')))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3277])).
% 123.15/16.46  thf(zip_derived_cl3294, plain, ( (in @ '#sk1599' @ '#sk1600')),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3285])).
% 123.15/16.46  thf(zip_derived_cl3295, plain, (~ (in @ '#sk1599' @ '#sk1597')),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3285])).
% 123.15/16.46  thf(zip_derived_cl1081, plain, ( (setminusILneg)),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1075])).
% 123.15/16.46  thf(setminusILneg, axiom, (setminusILneg) =>
% 123.15/16.46    ((((!!) @ (^[Y0 : $i]:
% 123.15/16.46                 (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                             (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                         (((((~) @ (in @ Y2 @ Y0))) =>
% 123.15/16.46                                           (((~) @ (in @ Y2 @ 
% 123.15/16.46                                                    (setminus @ Y0 @ Y1)))))))))))))))
% 123.15/16.46     = ($true))).
% 123.15/16.46  thf('4', plain,
% 123.15/16.46      (( setminusILneg ) <=>
% 123.15/16.46       ( ![X5:$i,X7:$i,X9:$i]:
% 123.15/16.46         ( ( ~( in @ X9 @ X5 ) ) => ( ~( in @ X9 @ ( setminus @ X5 @ X7 ) ) ) ) )),
% 123.15/16.46      inference('rw.lit', [status(esa)], [setminusILneg])).
% 123.15/16.46  thf(zip_derived_cl1087, plain,
% 123.15/16.46      ( (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                    (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                            (((((~) @ (in @ Y2 @ Y0))) =>
% 123.15/16.46                                              (((~) @ (in @ Y2 @ 
% 123.15/16.46                                                       (setminus @ Y0 @ Y1)))))))))))))))),
% 123.15/16.46      inference('rw_clause', [status(thm)], [zip_derived_cl1081, '4'])).
% 123.15/16.46  thf(zip_derived_cl1093, plain,
% 123.15/16.46      (![X2 : $i]:
% 123.15/16.46          (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                      (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                  (((((~) @ (in @ Y1 @ X2))) =>
% 123.15/16.46                                    (((~) @ (in @ Y1 @ (setminus @ X2 @ Y0))))))))))))),
% 123.15/16.46      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1087])).
% 123.15/16.46  thf(zip_derived_cl1099, plain,
% 123.15/16.46      (![X2 : $i, X4 : $i]:
% 123.15/16.46          (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                      (((((~) @ (in @ Y0 @ X2))) =>
% 123.15/16.46                        (((~) @ (in @ Y0 @ (setminus @ X2 @ X4)))))))))),
% 123.15/16.46      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1093])).
% 123.15/16.46  thf(zip_derived_cl1106, plain,
% 123.15/16.46      (![X2 : $i, X4 : $i, X6 : $i]:
% 123.15/16.46          (((((~) @ (in @ X6 @ X2))) =>
% 123.15/16.46            (((~) @ (in @ X6 @ (setminus @ X2 @ X4))))))),
% 123.15/16.46      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1099])).
% 123.15/16.46  thf(zip_derived_cl1113, plain,
% 123.15/16.46      (![X2 : $i, X4 : $i, X6 : $i]:
% 123.15/16.46         ( (in @ X6 @ X2) | ~ (in @ X6 @ (setminus @ X2 @ X4)))),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1106])).
% 123.15/16.46  thf(zip_derived_cl1001, plain, ( (binintersectER)),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl994])).
% 123.15/16.46  thf(binintersectER, axiom, (binintersectER) =>
% 123.15/16.46    ((((!!) @ (^[Y0 : $i]:
% 123.15/16.46                 (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                             (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                         (((in @ Y2 @ 
% 123.15/16.46                                           (binintersect @ Y0 @ Y1)) => (in @ 
% 123.15/16.46                                           Y2 @ Y1))))))))))))
% 123.15/16.46     = ($true))).
% 123.15/16.46  thf('5', plain,
% 123.15/16.46      (( binintersectER ) <=>
% 123.15/16.46       ( ![X5:$i,X7:$i,X9:$i]:
% 123.15/16.46         ( ( in @ X9 @ ( binintersect @ X5 @ X7 ) ) => ( in @ X9 @ X7 ) ) )),
% 123.15/16.46      inference('rw.lit', [status(esa)], [binintersectER])).
% 123.15/16.46  thf(zip_derived_cl1006, plain,
% 123.15/16.46      ( (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                    (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                            (((in @ Y2 @ 
% 123.15/16.46                                              (binintersect @ Y0 @ Y1)) =>
% 123.15/16.46                                              (in @ Y2 @ Y1))))))))))))),
% 123.15/16.46      inference('rw_clause', [status(thm)], [zip_derived_cl1001, '5'])).
% 123.15/16.46  thf(zip_derived_cl1011, plain,
% 123.15/16.46      (![X2 : $i]:
% 123.15/16.46          (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                      (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                  (((in @ Y1 @ (binintersect @ X2 @ Y0)) =>
% 123.15/16.46                                    (in @ Y1 @ Y0)))))))))),
% 123.15/16.46      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1006])).
% 123.15/16.46  thf(zip_derived_cl1017, plain,
% 123.15/16.46      (![X2 : $i, X4 : $i]:
% 123.15/16.46          (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                      (((in @ Y0 @ (binintersect @ X2 @ X4)) => (in @ Y0 @ X4))))))),
% 123.15/16.46      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl1011])).
% 123.15/16.46  thf(zip_derived_cl55, plain, ( (wellorderingAx)),
% 123.15/16.46      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl50])).
% 123.15/16.46  thf(wellorderingAx, axiom, (wellorderingAx) =>
% 123.15/16.46    ((((!!) @ (^[Y0 : $i]:
% 123.15/16.46                 (((??) @ (^[Y1 : $i]:
% 123.15/16.46                             (((((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                           (((in @ Y2 @ Y1) =>
% 123.15/16.46                                             (((!!) @ (^[Y3 : $i]:
% 123.15/16.46                                                         (((in @ Y3 @ Y2) =>
% 123.15/16.46                                                           (in @ Y3 @ Y0))))))))))) & 
% 123.15/16.46                               (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                           (((!!) @ (^[Y3 : $i]:
% 123.15/16.46                                                       (((((in @ Y3 @ Y0) &
% 123.15/16.46                                                           (in @ Y2 @ Y0))) =>
% 123.15/16.46                                                         (((((!!) @ (^[Y4 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y4 @ 
% 123.15/16.46                                                                      Y1) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y4) <=>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y3 @ Y4)))))))) =>
% 123.15/16.46                                                           (((Y2) = (Y3))))))))))))) & 
% 123.15/16.46                               (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                           (((!!) @ (^[Y3 : $i]:
% 123.15/16.46                                                       (((((in @ Y3 @ Y1) &
% 123.15/16.46                                                           (in @ Y2 @ Y1))) =>
% 123.15/16.46                                                         (((((!!) @ (^[Y4 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y4 @ 
% 123.15/16.46                                                                      Y3) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y4 @ Y2)))))) |
% 123.15/16.46                                                           (((!!) @ (^[Y4 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y4 @ 
% 123.15/16.46                                                                      Y2) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y4 @ Y3)))))))))))))))) & 
% 123.15/16.46                               (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                           (((((((??) @ (^[Y3 : $i]:
% 123.15/16.46                                                           (in @ Y3 @ Y2)))) &
% 123.15/16.46                                               (((!!) @ (^[Y3 : $i]:
% 123.15/16.46                                                           (((in @ Y3 @ Y2) =>
% 123.15/16.46                                                             (in @ Y3 @ Y0)))))))) =>
% 123.15/16.46                                             (((??) @ (^[Y3 : $i]:
% 123.15/16.46                                                         (((??) @ (^[Y4 : $i]:
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      in @ 
% 123.15/16.46                                                                      Y3 @ Y1) & 
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      in @ 
% 123.15/16.46                                                                      Y4 @ Y2) & 
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      (~) @ (
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      (??) @ (
% 123.15/16.46                                                                      ^[Y5 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y5 @ 
% 123.15/16.46                                                                      Y3) &
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y5 @ Y2)))))))) & 
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y5 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y5 @ 
% 123.15/16.46                                                                      Y1) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y4 @ 
% 123.15/16.46                                                                      Y5) |
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y6 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y6 @ 
% 123.15/16.46                                                                      Y5) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y6 @ Y3))))))))))))))))))))))))))))))))))
% 123.15/16.46     = ($true))).
% 123.15/16.46  thf('6', plain,
% 123.15/16.46      (( wellorderingAx ) <=>
% 123.15/16.46       ( ![X5:$i]:
% 123.15/16.46         ( ?[X7:$i]:
% 123.15/16.46           ( ( ![X9:$i]:
% 123.15/16.46               ( ( in @ X9 @ X7 ) =>
% 123.15/16.46                 ( ![X11:$i]: ( ( in @ X11 @ X9 ) => ( in @ X11 @ X5 ) ) ) ) ) & 
% 123.15/16.46             ( ![X13:$i,X15:$i]:
% 123.15/16.46               ( ( ( in @ X15 @ X5 ) & ( in @ X13 @ X5 ) ) =>
% 123.15/16.46                 ( ( ![X17:$i]:
% 123.15/16.46                     ( ( in @ X17 @ X7 ) =>
% 123.15/16.46                       ( ( in @ X13 @ X17 ) <=> ( in @ X15 @ X17 ) ) ) ) =>
% 123.15/16.46                   ( ( X13 ) = ( X15 ) ) ) ) ) & 
% 123.15/16.46             ( ![X19:$i,X21:$i]:
% 123.15/16.46               ( ( ( in @ X21 @ X7 ) & ( in @ X19 @ X7 ) ) =>
% 123.15/16.46                 ( ( ![X23:$i]: ( ( in @ X23 @ X21 ) => ( in @ X23 @ X19 ) ) ) | 
% 123.15/16.46                   ( ![X25:$i]: ( ( in @ X25 @ X19 ) => ( in @ X25 @ X21 ) ) ) ) ) ) & 
% 123.15/16.46             ( ![X27:$i]:
% 123.15/16.46               ( ( ( ?[X29:$i]: ( in @ X29 @ X27 ) ) & 
% 123.15/16.46                   ( ![X31:$i]: ( ( in @ X31 @ X27 ) => ( in @ X31 @ X5 ) ) ) ) =>
% 123.15/16.46                 ( ?[X33:$i,X35:$i]:
% 123.15/16.46                   ( ( in @ X33 @ X7 ) & ( in @ X35 @ X27 ) & 
% 123.15/16.46                     ( ~( ?[X37:$i]:
% 123.15/16.46                          ( ( in @ X37 @ X33 ) & ( in @ X37 @ X27 ) ) ) ) & 
% 123.15/16.46                     ( ![X39:$i]:
% 123.15/16.46                       ( ( in @ X39 @ X7 ) =>
% 123.15/16.46                         ( ( in @ X35 @ X39 ) | 
% 123.15/16.46                           ( ![X41:$i]:
% 123.15/16.46                             ( ( in @ X41 @ X39 ) => ( in @ X41 @ X33 ) ) ) ) ) ) ) ) ) ) ) ) )),
% 123.15/16.46      inference('rw.lit', [status(esa)], [wellorderingAx])).
% 123.15/16.46  thf(zip_derived_cl60, plain,
% 123.15/16.46      ( (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                    (((??) @ (^[Y1 : $i]:
% 123.15/16.46                                (((((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                              (((in @ Y2 @ Y1) =>
% 123.15/16.46                                                (((!!) @ (^[Y3 : $i]:
% 123.15/16.46                                                            (((in @ Y3 @ Y2) =>
% 123.15/16.46                                                              (in @ Y3 @ Y0))))))))))) & 
% 123.15/16.46                                  (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                              (((!!) @ (^[Y3 : $i]:
% 123.15/16.46                                                          (((((in @ Y3 @ Y0) &
% 123.15/16.46                                                              (in @ Y2 @ Y0))) =>
% 123.15/16.46                                                            (((((!!) @ (
% 123.15/16.46                                                                ^[Y4 : $i]:
% 123.15/16.46                                                                  (((in @ Y4 @ 
% 123.15/16.46                                                                    Y1) =>
% 123.15/16.46                                                                    (((in @ 
% 123.15/16.46                                                                      Y2 @ 
% 123.15/16.46                                                                      Y4) <=>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y3 @ Y4)))))))) =>
% 123.15/16.46                                                              (((Y2) = (Y3))))))))))))) & 
% 123.15/16.46                                  (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                              (((!!) @ (^[Y3 : $i]:
% 123.15/16.46                                                          (((((in @ Y3 @ Y1) &
% 123.15/16.46                                                              (in @ Y2 @ Y1))) =>
% 123.15/16.46                                                            (((((!!) @ (
% 123.15/16.46                                                                ^[Y4 : $i]:
% 123.15/16.46                                                                  (((in @ Y4 @ 
% 123.15/16.46                                                                    Y3) =>
% 123.15/16.46                                                                    (in @ Y4 @ 
% 123.15/16.46                                                                    Y2)))))) |
% 123.15/16.46                                                              (((!!) @ (
% 123.15/16.46                                                                ^[Y4 : $i]:
% 123.15/16.46                                                                  (((in @ Y4 @ 
% 123.15/16.46                                                                    Y2) =>
% 123.15/16.46                                                                    (in @ Y4 @ 
% 123.15/16.46                                                                    Y3)))))))))))))))) & 
% 123.15/16.46                                  (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                              (((((((??) @ (^[Y3 : $i]:
% 123.15/16.46                                                              (in @ Y3 @ Y2)))) &
% 123.15/16.46                                                  (((!!) @ (^[Y3 : $i]:
% 123.15/16.46                                                              (((in @ Y3 @ 
% 123.15/16.46                                                                Y2) => (in @ 
% 123.15/16.46                                                                Y3 @ Y0)))))))) =>
% 123.15/16.46                                                (((??) @ (^[Y3 : $i]:
% 123.15/16.46                                                            (((??) @ (^[Y4 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      in @ 
% 123.15/16.46                                                                      Y3 @ Y1) & 
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      in @ 
% 123.15/16.46                                                                      Y4 @ Y2) & 
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      (~) @ (
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      (??) @ (
% 123.15/16.46                                                                      ^[Y5 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y5 @ 
% 123.15/16.46                                                                      Y3) &
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y5 @ Y2)))))))) & 
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y5 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y5 @ 
% 123.15/16.46                                                                      Y1) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y4 @ 
% 123.15/16.46                                                                      Y5) |
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y6 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y6 @ 
% 123.15/16.46                                                                      Y5) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y6 @ Y3))))))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('rw_clause', [status(thm)], [zip_derived_cl55, '6'])).
% 123.15/16.46  thf(zip_derived_cl66, plain,
% 123.15/16.46      (![X2 : $i]:
% 123.15/16.46          (((??) @ (^[Y0 : $i]:
% 123.15/16.46                      (((((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                    (((in @ Y1 @ Y0) =>
% 123.15/16.46                                      (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                  (((in @ Y2 @ Y1) => (in @ 
% 123.15/16.46                                                    Y2 @ X2))))))))))) & 
% 123.15/16.46                        (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                    (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                (((((in @ Y2 @ X2) & (in @ 
% 123.15/16.46                                                    Y1 @ X2))) =>
% 123.15/16.46                                                  (((((!!) @ (^[Y3 : $i]:
% 123.15/16.46                                                                (((in @ Y3 @ 
% 123.15/16.46                                                                  Y0) =>
% 123.15/16.46                                                                  (((in @ Y1 @ 
% 123.15/16.46                                                                    Y3) <=>
% 123.15/16.46                                                                    (in @ Y2 @ 
% 123.15/16.46                                                                    Y3)))))))) =>
% 123.15/16.46                                                    (((Y1) = (Y2))))))))))))) & 
% 123.15/16.46                        (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                    (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                (((((in @ Y2 @ Y0) & (in @ 
% 123.15/16.46                                                    Y1 @ Y0))) =>
% 123.15/16.46                                                  (((((!!) @ (^[Y3 : $i]:
% 123.15/16.46                                                                (((in @ Y3 @ 
% 123.15/16.46                                                                  Y2) => (in @ 
% 123.15/16.46                                                                  Y3 @ Y1)))))) |
% 123.15/16.46                                                    (((!!) @ (^[Y3 : $i]:
% 123.15/16.46                                                                (((in @ Y3 @ 
% 123.15/16.46                                                                  Y1) => (in @ 
% 123.15/16.46                                                                  Y3 @ Y2)))))))))))))))) & 
% 123.15/16.46                        (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                    (((((((??) @ (^[Y2 : $i]: (in @ Y2 @ Y1)))) &
% 123.15/16.46                                        (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                    (((in @ Y2 @ Y1) => (in @ 
% 123.15/16.46                                                      Y2 @ X2)))))))) =>
% 123.15/16.46                                      (((??) @ (^[Y2 : $i]:
% 123.15/16.46                                                  (((??) @ (^[Y3 : $i]:
% 123.15/16.46                                                              (((in @ Y2 @ Y0) & 
% 123.15/16.46                                                                (in @ Y3 @ Y1) & 
% 123.15/16.46                                                                (((~) @ (
% 123.15/16.46                                                                  ((??) @ (
% 123.15/16.46                                                                   ^[Y4 : $i]:
% 123.15/16.46                                                                     ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y4 @ 
% 123.15/16.46                                                                      Y2) &
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y4 @ Y1)))))))) & 
% 123.15/16.46                                                                (((!!) @ (
% 123.15/16.46                                                                  ^[Y4 : $i]:
% 123.15/16.46                                                                    (((in @ 
% 123.15/16.46                                                                      Y4 @ 
% 123.15/16.46                                                                      Y0) =>
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y3 @ 
% 123.15/16.46                                                                      Y4) |
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (!!) @ (
% 123.15/16.46                                                                      ^[Y5 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y5 @ 
% 123.15/16.46                                                                      Y4) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y5 @ Y2)))))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl60])).
% 123.15/16.46  thf(zip_derived_cl74, plain,
% 123.15/16.46      (![X2 : $i]:
% 123.15/16.46          (((((!!) @ (^[Y0 : $i]:
% 123.15/16.46                        (((in @ Y0 @ ('#sk16' @ X2)) =>
% 123.15/16.46                          (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                      (((in @ Y1 @ Y0) => (in @ Y1 @ X2))))))))))) & 
% 123.15/16.46            (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                        (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                    (((((in @ Y1 @ X2) & (in @ Y0 @ X2))) =>
% 123.15/16.46                                      (((((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                    (((in @ Y2 @ 
% 123.15/16.46                                                      ('#sk16' @ X2)) =>
% 123.15/16.46                                                      (((in @ Y0 @ Y2) <=>
% 123.15/16.46                                                        (in @ Y1 @ Y2)))))))) =>
% 123.15/16.46                                        (((Y0) = (Y1))))))))))))) & 
% 123.15/16.46            (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                        (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                    (((((in @ Y1 @ ('#sk16' @ X2)) & (in @ 
% 123.15/16.46                                        Y0 @ ('#sk16' @ X2)))) =>
% 123.15/16.46                                      (((((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                    (((in @ Y2 @ Y1) => (in @ 
% 123.15/16.46                                                      Y2 @ Y0)))))) |
% 123.15/16.46                                        (((!!) @ (^[Y2 : $i]:
% 123.15/16.46                                                    (((in @ Y2 @ Y0) => (in @ 
% 123.15/16.46                                                      Y2 @ Y1)))))))))))))))) & 
% 123.15/16.46            (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                        (((((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) &
% 123.15/16.46                            (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                        (((in @ Y1 @ Y0) => (in @ Y1 @ X2)))))))) =>
% 123.15/16.46                          (((??) @ (^[Y1 : $i]:
% 123.15/16.46                                      (((??) @ (^[Y2 : $i]:
% 123.15/16.46                                                  (((in @ Y1 @ ('#sk16' @ X2)) & 
% 123.15/16.46                                                    (in @ Y2 @ Y0) & 
% 123.15/16.46                                                    (((~) @ (((??) @ (^[Y3 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y3 @ 
% 123.15/16.46                                                                      Y1) &
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y3 @ Y0)))))))) & 
% 123.15/16.46                                                    (((!!) @ (^[Y3 : $i]:
% 123.15/16.46                                                                (((in @ Y3 @ 
% 123.15/16.46                                                                  ('#sk16' @ X2)) =>
% 123.15/16.46                                                                  (((in @ Y2 @ 
% 123.15/16.46                                                                    Y3) |
% 123.15/16.46                                                                    (((!!) @ (
% 123.15/16.46                                                                      ^[Y4 : $i]:
% 123.15/16.46                                                                      ((
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y4 @ 
% 123.15/16.46                                                                      Y3) =>
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y4 @ Y1))))))))))))))))))))))))))))),
% 123.15/16.46      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl66])).
% 123.15/16.46  thf(zip_derived_cl89, plain,
% 123.15/16.46      (![X2 : $i]:
% 123.15/16.46          (((!!) @ (^[Y0 : $i]:
% 123.15/16.46                      (((((((??) @ (^[Y1 : $i]: (in @ Y1 @ Y0)))) &
% 123.15/16.46                          (((!!) @ (^[Y1 : $i]:
% 123.15/16.46                                      (((in @ Y1 @ Y0) => (in @ Y1 @ X2)))))))) =>
% 123.15/16.46                        (((??) @ (^[Y1 : $i]:
% 123.15/16.46                                    (((??) @ (^[Y2 : $i]:
% 123.15/16.46                                                (((in @ Y1 @ ('#sk16' @ X2)) & 
% 123.15/16.46                                                  (in @ Y2 @ Y0) & 
% 123.15/16.46                                                  (((~) @ (((??) @ (^[Y3 : $i]:
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      (
% 123.15/16.46                                                                      (in @ 
% 123.15/16.46                                                                      Y3 @ 
% 123.15/16.46                                                                      Y1) &
% 123.15/16.46                                                                      (in @ 
% 123.15/16.47                                                                      Y3 @ Y0)))))))) & 
% 123.15/16.47                                                  (((!!) @ (^[Y3 : $i]:
% 123.15/16.47                                                              (((in @ Y3 @ 
% 123.15/16.47                                                                ('#sk16' @ X2)) =>
% 123.15/16.47                                                                (((in @ Y2 @ 
% 123.15/16.47                                                                  Y3) |
% 123.15/16.47                                                                  (((!!) @ (
% 123.15/16.47                                                                    ^[Y4 : $i]:
% 123.15/16.47                                                                      (
% 123.15/16.47                                                                      (
% 123.15/16.47                                                                      (in @ 
% 123.15/16.47                                                                      Y4 @ 
% 123.15/16.47                                                                      Y3) =>
% 123.15/16.47                                                                      (in @ 
% 123.15/16.47                                                                      Y4 @ Y1))))))))))))))))))))))))))),
% 123.15/16.47      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl74])).
% 123.15/16.47  thf(zip_derived_cl108, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47          (((((((??) @ (^[Y0 : $i]: (in @ Y0 @ X4)))) &
% 123.15/16.47              (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))) =>
% 123.15/16.47            (((??) @ (^[Y0 : $i]:
% 123.15/16.47                        (((??) @ (^[Y1 : $i]:
% 123.15/16.47                                    (((in @ Y0 @ ('#sk16' @ X2)) & 
% 123.15/16.47                                      (in @ Y1 @ X4) & 
% 123.15/16.47                                      (((~) @ (((??) @ (^[Y2 : $i]:
% 123.15/16.47                                                          (((in @ Y2 @ Y0) &
% 123.15/16.47                                                            (in @ Y2 @ X4)))))))) & 
% 123.15/16.47                                      (((!!) @ (^[Y2 : $i]:
% 123.15/16.47                                                  (((in @ Y2 @ 
% 123.15/16.47                                                    ('#sk16' @ X2)) =>
% 123.15/16.47                                                    (((in @ Y1 @ Y2) |
% 123.15/16.47                                                      (((!!) @ (^[Y3 : $i]:
% 123.15/16.47                                                                  (((in @ Y3 @ 
% 123.15/16.47                                                                    Y2) =>
% 123.15/16.47                                                                    (in @ Y3 @ 
% 123.15/16.47                                                                    Y0)))))))))))))))))))))))),
% 123.15/16.47      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl89])).
% 123.15/16.47  thf(zip_derived_cl125, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         (~ (((((??) @ (^[Y0 : $i]: (in @ Y0 @ X4)))) &
% 123.15/16.47              (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2))))))))
% 123.15/16.47          |  (((??) @ (^[Y0 : $i]:
% 123.15/16.47                         (((??) @ (^[Y1 : $i]:
% 123.15/16.47                                     (((in @ Y0 @ ('#sk16' @ X2)) & 
% 123.15/16.47                                       (in @ Y1 @ X4) & 
% 123.15/16.47                                       (((~) @ (((??) @ (^[Y2 : $i]:
% 123.15/16.47                                                           (((in @ Y2 @ Y0) &
% 123.15/16.47                                                             (in @ Y2 @ X4)))))))) & 
% 123.15/16.47                                       (((!!) @ (^[Y2 : $i]:
% 123.15/16.47                                                   (((in @ Y2 @ 
% 123.15/16.47                                                     ('#sk16' @ X2)) =>
% 123.15/16.47                                                     (((in @ Y1 @ Y2) |
% 123.15/16.47                                                       (((!!) @ (^[Y3 : $i]:
% 123.15/16.47                                                                   (((in @ 
% 123.15/16.47                                                                     Y3 @ 
% 123.15/16.47                                                                     Y2) =>
% 123.15/16.47                                                                     (in @ 
% 123.15/16.47                                                                     Y3 @ Y0))))))))))))))))))))))),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl108])).
% 123.15/16.47  thf(zip_derived_cl140, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         (~ (((??) @ (^[Y0 : $i]: (in @ Y0 @ X4))))
% 123.15/16.47          | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2))))))
% 123.15/16.47          |  (((??) @ (^[Y0 : $i]:
% 123.15/16.47                         (((??) @ (^[Y1 : $i]:
% 123.15/16.47                                     (((in @ Y0 @ ('#sk16' @ X2)) & 
% 123.15/16.47                                       (in @ Y1 @ X4) & 
% 123.15/16.47                                       (((~) @ (((??) @ (^[Y2 : $i]:
% 123.15/16.47                                                           (((in @ Y2 @ Y0) &
% 123.15/16.47                                                             (in @ Y2 @ X4)))))))) & 
% 123.15/16.47                                       (((!!) @ (^[Y2 : $i]:
% 123.15/16.47                                                   (((in @ Y2 @ 
% 123.15/16.47                                                     ('#sk16' @ X2)) =>
% 123.15/16.47                                                     (((in @ Y1 @ Y2) |
% 123.15/16.47                                                       (((!!) @ (^[Y3 : $i]:
% 123.15/16.47                                                                   (((in @ 
% 123.15/16.47                                                                     Y3 @ 
% 123.15/16.47                                                                     Y2) =>
% 123.15/16.47                                                                     (in @ 
% 123.15/16.47                                                                     Y3 @ Y0))))))))))))))))))))))),
% 123.15/16.47      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl125])).
% 123.15/16.47  thf(zip_derived_cl155, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i, X6 : $i]:
% 123.15/16.47         (~ (in @ X6 @ X4)
% 123.15/16.47          |  (((??) @ (^[Y0 : $i]:
% 123.15/16.47                         (((??) @ (^[Y1 : $i]:
% 123.15/16.47                                     (((in @ Y0 @ ('#sk16' @ X2)) & 
% 123.15/16.47                                       (in @ Y1 @ X4) & 
% 123.15/16.47                                       (((~) @ (((??) @ (^[Y2 : $i]:
% 123.15/16.47                                                           (((in @ Y2 @ Y0) &
% 123.15/16.47                                                             (in @ Y2 @ X4)))))))) & 
% 123.15/16.47                                       (((!!) @ (^[Y2 : $i]:
% 123.15/16.47                                                   (((in @ Y2 @ 
% 123.15/16.47                                                     ('#sk16' @ X2)) =>
% 123.15/16.47                                                     (((in @ Y1 @ Y2) |
% 123.15/16.47                                                       (((!!) @ (^[Y3 : $i]:
% 123.15/16.47                                                                   (((in @ 
% 123.15/16.47                                                                     Y3 @ 
% 123.15/16.47                                                                     Y2) =>
% 123.15/16.47                                                                     (in @ 
% 123.15/16.47                                                                     Y3 @ Y0)))))))))))))))))))))
% 123.15/16.47          | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))),
% 123.15/16.47      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl140])).
% 123.15/16.47  thf(zip_derived_cl168, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i, X6 : $i]:
% 123.15/16.47         ( (((??) @ (^[Y0 : $i]:
% 123.15/16.47                       (((in @ ('#sk111' @ X2 @ X4) @ ('#sk16' @ X2)) & 
% 123.15/16.47                         (in @ Y0 @ X4) & 
% 123.15/16.47                         (((~) @ (((??) @ (^[Y1 : $i]:
% 123.15/16.47                                             (((in @ Y1 @ 
% 123.15/16.47                                               ('#sk111' @ X2 @ X4)) & (in @ 
% 123.15/16.47                                               Y1 @ X4)))))))) & 
% 123.15/16.47                         (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                                     (((in @ Y1 @ ('#sk16' @ X2)) =>
% 123.15/16.47                                       (((in @ Y0 @ Y1) |
% 123.15/16.47                                         (((!!) @ (^[Y2 : $i]:
% 123.15/16.47                                                     (((in @ Y2 @ Y1) => (in @ 
% 123.15/16.47                                                       Y2 @ 
% 123.15/16.47                                                       ('#sk111' @ X2 @ X4)))))))))))))))))))
% 123.15/16.47          | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2))))))
% 123.15/16.47          | ~ (in @ X6 @ X4))),
% 123.15/16.47      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl155])).
% 123.15/16.47  thf(zip_derived_cl183, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i, X6 : $i]:
% 123.15/16.47         ( (((in @ ('#sk111' @ X2 @ X4) @ ('#sk16' @ X2)) & 
% 123.15/16.47             (in @ ('#sk134' @ X2 @ X4) @ X4) & 
% 123.15/16.47             (((~) @ (((??) @ (^[Y0 : $i]:
% 123.15/16.47                                 (((in @ Y0 @ ('#sk111' @ X2 @ X4)) & (in @ 
% 123.15/16.47                                   Y0 @ X4)))))))) & 
% 123.15/16.47             (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                         (((in @ Y0 @ ('#sk16' @ X2)) =>
% 123.15/16.47                           (((in @ ('#sk134' @ X2 @ X4) @ Y0) |
% 123.15/16.47                             (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                                         (((in @ Y1 @ Y0) => (in @ Y1 @ 
% 123.15/16.47                                           ('#sk111' @ X2 @ X4))))))))))))))))
% 123.15/16.47          | ~ (in @ X6 @ X4)
% 123.15/16.47          | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))),
% 123.15/16.47      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl168])).
% 123.15/16.47  thf(zip_derived_cl199, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i, X6 : $i]:
% 123.15/16.47         ( (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                       (((in @ Y0 @ ('#sk16' @ X2)) =>
% 123.15/16.47                         (((in @ ('#sk134' @ X2 @ X4) @ Y0) |
% 123.15/16.47                           (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                                       (((in @ Y1 @ Y0) => (in @ Y1 @ 
% 123.15/16.47                                         ('#sk111' @ X2 @ X4))))))))))))))
% 123.15/16.47          | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2))))))
% 123.15/16.47          | ~ (in @ X6 @ X4))),
% 123.15/16.47      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl183])).
% 123.15/16.47  thf(zip_derived_cl196, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i, X6 : $i]:
% 123.15/16.47         ( (in @ ('#sk111' @ X2 @ X4) @ ('#sk16' @ X2))
% 123.15/16.47          | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2))))))
% 123.15/16.47          | ~ (in @ X6 @ X4))),
% 123.15/16.47      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl183])).
% 123.15/16.47  thf(zip_derived_cl208, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         ( ('#form172' @ X2 @ X4)
% 123.15/16.47          | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))),
% 123.15/16.47      define([status(thm)])).
% 123.15/16.47  thf(zip_derived_cl213, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i, X6 : $i]:
% 123.15/16.47         (~ ('#form172' @ X2 @ X4)
% 123.15/16.47          | ~ (in @ X6 @ X4)
% 123.15/16.47          |  (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                         (((in @ Y0 @ ('#sk16' @ X2)) =>
% 123.15/16.47                           (((in @ ('#sk134' @ X2 @ X4) @ Y0) |
% 123.15/16.47                             (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                                         (((in @ Y1 @ Y0) => (in @ Y1 @ 
% 123.15/16.47                                           ('#sk111' @ X2 @ X4)))))))))))))))),
% 123.15/16.47      inference('renaming', [status(thm)],
% 123.15/16.47                [zip_derived_cl199, zip_derived_cl208])).
% 123.15/16.47  thf(zip_derived_cl224, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 123.15/16.47         ( (((in @ X8 @ ('#sk16' @ X2)) =>
% 123.15/16.47             (((in @ ('#sk134' @ X2 @ X4) @ X8) |
% 123.15/16.47               (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                           (((in @ Y0 @ X8) => (in @ Y0 @ ('#sk111' @ X2 @ X4)))))))))))
% 123.15/16.47          | ~ (in @ X6 @ X4)
% 123.15/16.47          | ~ ('#form172' @ X2 @ X4))),
% 123.15/16.47      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl213])).
% 123.15/16.47  thf(zip_derived_cl233, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 123.15/16.47         (~ (in @ X8 @ ('#sk16' @ X2))
% 123.15/16.47          |  (((in @ ('#sk134' @ X2 @ X4) @ X8) |
% 123.15/16.47               (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                           (((in @ Y0 @ X8) => (in @ Y0 @ ('#sk111' @ X2 @ X4)))))))))
% 123.15/16.47          | ~ ('#form172' @ X2 @ X4)
% 123.15/16.47          | ~ (in @ X6 @ X4))),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl224])).
% 123.15/16.47  thf(zip_derived_cl246, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i, X6 : $i, X8 : $i]:
% 123.15/16.47         ( (in @ ('#sk134' @ X2 @ X4) @ X8)
% 123.15/16.47          |  (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                         (((in @ Y0 @ X8) => (in @ Y0 @ ('#sk111' @ X2 @ X4)))))))
% 123.15/16.47          | ~ (in @ X6 @ X4)
% 123.15/16.47          | ~ ('#form172' @ X2 @ X4)
% 123.15/16.47          | ~ (in @ X8 @ ('#sk16' @ X2)))),
% 123.15/16.47      inference('lazy_cnf_or', [status(thm)], [zip_derived_cl233])).
% 123.15/16.47  thf(zip_derived_cl259, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         (~ ('#form172' @ X2 @ X4)
% 123.15/16.47          |  (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))),
% 123.15/16.47      define([status(thm)])).
% 123.15/16.47  thf(zip_derived_cl208, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         ( ('#form172' @ X2 @ X4)
% 123.15/16.47          | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))),
% 123.15/16.47      define([status(thm)])).
% 123.15/16.47  thf(zip_derived_cl1023, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:  ('#form172' @ X4 @ (binintersect @ X2 @ X4))),
% 123.15/16.47      inference('renaming', [status(thm)],
% 123.15/16.47                [zip_derived_cl1017, zip_derived_cl259, zip_derived_cl208])).
% 123.15/16.47  thf(zip_derived_cl2309, plain, ( (doubleComplementEq)),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2299])).
% 123.15/16.47  thf(doubleComplementEq, axiom, (doubleComplementEq) =>
% 123.15/16.47    ((((!!) @ (^[Y0 : $i]:
% 123.15/16.47                 (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                             (((in @ Y1 @ (powerset @ Y0)) =>
% 123.15/16.47                               (((Y1) = (setminus @ Y0 @ (setminus @ Y0 @ Y1))))))))))))
% 123.15/16.47     = ($true))).
% 123.15/16.47  thf('7', plain,
% 123.15/16.47      (( doubleComplementEq ) <=>
% 123.15/16.47       ( ![X5:$i,X7:$i]:
% 123.15/16.47         ( ( in @ X7 @ ( powerset @ X5 ) ) =>
% 123.15/16.47           ( ( X7 ) = ( setminus @ X5 @ ( setminus @ X5 @ X7 ) ) ) ) )),
% 123.15/16.47      inference('rw.lit', [status(esa)], [doubleComplementEq])).
% 123.15/16.47  thf(zip_derived_cl2319, plain,
% 123.15/16.47      ( (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                    (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                                (((in @ Y1 @ (powerset @ Y0)) =>
% 123.15/16.47                                  (((Y1) = (setminus @ Y0 @ 
% 123.15/16.47                                    (setminus @ Y0 @ Y1))))))))))))),
% 123.15/16.47      inference('rw_clause', [status(thm)], [zip_derived_cl2309, '7'])).
% 123.15/16.47  thf(zip_derived_cl2329, plain,
% 123.15/16.47      (![X2 : $i]:
% 123.15/16.47          (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                      (((in @ Y0 @ (powerset @ X2)) =>
% 123.15/16.47                        (((Y0) = (setminus @ X2 @ (setminus @ X2 @ Y0)))))))))),
% 123.15/16.47      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2319])).
% 123.15/16.47  thf(zip_derived_cl2337, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47          (((in @ X4 @ (powerset @ X2)) =>
% 123.15/16.47            (((X4) = (setminus @ X2 @ (setminus @ X2 @ X4))))))),
% 123.15/16.47      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl2329])).
% 123.15/16.47  thf(zip_derived_cl2343, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         (~ (in @ X4 @ (powerset @ X2))
% 123.15/16.47          |  (((X4) = (setminus @ X2 @ (setminus @ X2 @ X4)))))),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl2337])).
% 123.15/16.47  thf(zip_derived_cl2349, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         (~ (in @ X4 @ (powerset @ X2))
% 123.15/16.47          | ((X4) = (setminus @ X2 @ (setminus @ X2 @ X4))))),
% 123.15/16.47      inference('simplify nested equalities', [status(thm)],
% 123.15/16.47                [zip_derived_cl2343])).
% 123.15/16.47  thf(zip_derived_cl15, plain, ( (powersetAx)),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl11])).
% 123.15/16.47  thf(powersetAx, axiom, (powersetAx) =>
% 123.15/16.47    ((((!!) @ (^[Y0 : $i]:
% 123.15/16.47                 (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                             (((in @ Y1 @ (powerset @ Y0)) <=>
% 123.15/16.47                               (((!!) @ (^[Y2 : $i]:
% 123.15/16.47                                           (((in @ Y2 @ Y1) => (in @ Y2 @ Y0))))))))))))))
% 123.15/16.47     = ($true))).
% 123.15/16.47  thf('8', plain,
% 123.15/16.47      (( powersetAx ) <=>
% 123.15/16.47       ( ![X5:$i,X7:$i]:
% 123.15/16.47         ( ( in @ X7 @ ( powerset @ X5 ) ) <=>
% 123.15/16.47           ( ![X9:$i]: ( ( in @ X9 @ X7 ) => ( in @ X9 @ X5 ) ) ) ) )),
% 123.15/16.47      inference('rw.lit', [status(esa)], [powersetAx])).
% 123.15/16.47  thf(zip_derived_cl19, plain,
% 123.15/16.47      ( (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                    (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                                (((in @ Y1 @ (powerset @ Y0)) <=>
% 123.15/16.47                                  (((!!) @ (^[Y2 : $i]:
% 123.15/16.47                                              (((in @ Y2 @ Y1) => (in @ Y2 @ 
% 123.15/16.47                                                Y0))))))))))))))),
% 123.15/16.47      inference('rw_clause', [status(thm)], [zip_derived_cl15, '8'])).
% 123.15/16.47  thf(zip_derived_cl25, plain,
% 123.15/16.47      (![X2 : $i]:
% 123.15/16.47          (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                      (((in @ Y0 @ (powerset @ X2)) <=>
% 123.15/16.47                        (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                                    (((in @ Y1 @ Y0) => (in @ Y1 @ X2)))))))))))),
% 123.15/16.47      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl19])).
% 123.15/16.47  thf(zip_derived_cl31, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47          (((in @ X4 @ (powerset @ X2)) <=>
% 123.15/16.47            (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2))))))))),
% 123.15/16.47      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl25])).
% 123.15/16.47  thf(zip_derived_cl36, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         ((in @ X4 @ (powerset @ X2))
% 123.15/16.47           = (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))),
% 123.15/16.47      inference('simplify nested equalities', [status(thm)], [zip_derived_cl31])).
% 123.15/16.47  thf(zip_derived_cl259, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         (~ ('#form172' @ X2 @ X4)
% 123.15/16.47          |  (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))),
% 123.15/16.47      define([status(thm)])).
% 123.15/16.47  thf(zip_derived_cl208, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         ( ('#form172' @ X2 @ X4)
% 123.15/16.47          | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X4) => (in @ Y0 @ X2)))))))),
% 123.15/16.47      define([status(thm)])).
% 123.15/16.47  thf(zip_derived_cl3403, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47          (((in @ X4 @ (powerset @ X2)) = ('#form172' @ X2 @ X4)))),
% 123.15/16.47      inference('renaming', [status(thm)],
% 123.15/16.47                [zip_derived_cl36, zip_derived_cl259, zip_derived_cl208])).
% 123.15/16.47  thf(zip_derived_cl3404, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         ((in @ X4 @ (powerset @ X2)) = ('#form172' @ X2 @ X4))),
% 123.15/16.47      inference('simplify nested equalities', [status(thm)],
% 123.15/16.47                [zip_derived_cl3403])).
% 123.15/16.47  thf(zip_derived_cl3419, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         (~ ('#form172' @ X2 @ X4)
% 123.15/16.47          | ((X4) = (setminus @ X2 @ (setminus @ X2 @ X4))))),
% 123.15/16.47      inference('demod', [status(thm)],
% 123.15/16.47                [zip_derived_cl2349, zip_derived_cl3404])).
% 123.15/16.47  thf(zip_derived_cl3256, plain, ( (ordinal @ '#sk1597')),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3246])).
% 123.15/16.47  thf(ordinal, axiom, (ordinal @ X0) =>
% 123.15/16.47    ((((wellorderedByIn @ X0) & (transitiveset @ X0))) = ($true))).
% 123.15/16.47  thf('9', plain,
% 123.15/16.47      (![X0:$i]:
% 123.15/16.47       ( ( ordinal @ X0 ) <=>
% 123.15/16.47         ( ( transitiveset @ X0 ) & ( wellorderedByIn @ X0 ) ) )),
% 123.15/16.47      inference('rw.lit', [status(esa)], [ordinal])).
% 123.15/16.47  thf(zip_derived_cl3268, plain,
% 123.15/16.47      ( (((wellorderedByIn @ '#sk1597') & (transitiveset @ '#sk1597')))),
% 123.15/16.47      inference('rw_clause', [status(thm)], [zip_derived_cl3256, '9'])).
% 123.15/16.47  thf(zip_derived_cl3276, plain, ( (transitiveset @ '#sk1597')),
% 123.15/16.47      inference('lazy_cnf_and', [status(thm)], [zip_derived_cl3268])).
% 123.15/16.47  thf(transitiveset, axiom, (transitiveset @ X0) =>
% 123.15/16.47    ((((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))) =
% 123.15/16.47     ($true))).
% 123.15/16.47  thf('10', plain,
% 123.15/16.47      (![X0:$i]:
% 123.15/16.47       ( ( transitiveset @ X0 ) <=>
% 123.15/16.47         ( ![X5:$i]: ( ( in @ X5 @ X0 ) => ( subset @ X5 @ X0 ) ) ) )),
% 123.15/16.47      inference('rw.lit', [status(esa)], [transitiveset])).
% 123.15/16.47  thf(zip_derived_cl3283, plain,
% 123.15/16.47      ( (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                    (((in @ Y0 @ '#sk1597') => (subset @ Y0 @ '#sk1597'))))))),
% 123.15/16.47      inference('rw_clause', [status(thm)], [zip_derived_cl3276, '10'])).
% 123.15/16.47  thf(zip_derived_cl3210, plain, ( (transitivesetOp1)),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3205])).
% 123.15/16.47  thf(transitivesetOp1, axiom, (transitivesetOp1) =>
% 123.15/16.47    ((((!!) @ (^[Y0 : $i]:
% 123.15/16.47                 (((transitiveset @ Y0) =>
% 123.15/16.47                   (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                               (((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))))))))))
% 123.15/16.47     = ($true))).
% 123.15/16.47  thf('11', plain,
% 123.15/16.47      (( transitivesetOp1 ) <=>
% 123.15/16.47       ( ![X5:$i]:
% 123.15/16.47         ( ( transitiveset @ X5 ) =>
% 123.15/16.47           ( ![X7:$i]: ( ( in @ X7 @ X5 ) => ( subset @ X7 @ X5 ) ) ) ) )),
% 123.15/16.47      inference('rw.lit', [status(esa)], [transitivesetOp1])).
% 123.15/16.47  thf(zip_derived_cl3215, plain,
% 123.15/16.47      ( (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                    (((transitiveset @ Y0) =>
% 123.15/16.47                      (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                                  (((in @ Y1 @ Y0) => (subset @ Y1 @ Y0)))))))))))),
% 123.15/16.47      inference('rw_clause', [status(thm)], [zip_derived_cl3210, '11'])).
% 123.15/16.47  thf(zip_derived_cl3222, plain,
% 123.15/16.47      (![X2 : $i]:
% 123.15/16.47          (((transitiveset @ X2) =>
% 123.15/16.47            (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (subset @ Y0 @ X2))))))))),
% 123.15/16.47      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3215])).
% 123.15/16.47  thf(zip_derived_cl3228, plain,
% 123.15/16.47      (![X2 : $i]:
% 123.15/16.47         (~ (transitiveset @ X2)
% 123.15/16.47          |  (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X2) => (subset @ Y0 @ X2)))))))),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3222])).
% 123.15/16.47  thf(transitiveset, axiom, ~ (transitiveset @ X0) =>
% 123.15/16.47    ((((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))) !=
% 123.15/16.47     ($true))).
% 123.15/16.47  thf('12', plain,
% 123.15/16.47      (![X0:$i]:
% 123.15/16.47       ( ( ~( transitiveset @ X0 ) ) <=>
% 123.15/16.47         ( ~( ![X5:$i]: ( ( in @ X5 @ X0 ) => ( subset @ X5 @ X0 ) ) ) ) )),
% 123.15/16.47      inference('rw.lit', [status(esa)], [transitiveset])).
% 123.15/16.47  thf(zip_derived_cl3234, plain,
% 123.15/16.47      (![X0 : $i]:
% 123.15/16.47         (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0))))))
% 123.15/16.47          |  (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 123.15/16.47      inference('rw_clause', [status(thm)], [zip_derived_cl3228, '12'])).
% 123.15/16.47  thf(zip_derived_cl3241, plain,
% 123.15/16.47      (![X0 : $i]:
% 123.15/16.47         (~ (((in @ ('#sk337' @ X0 @ (^[Y0 : $i]: (subset @ Y0 @ X0))) @ X0) =>
% 123.15/16.47              (subset @ ('#sk337' @ X0 @ (^[Y0 : $i]: (subset @ Y0 @ X0))) @ 
% 123.15/16.47              X0)))
% 123.15/16.47          |  (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 123.15/16.47      inference('lazy_cnf_exists', [status(thm)], [zip_derived_cl3234])).
% 123.15/16.47  thf(zip_derived_cl3248, plain,
% 123.15/16.47      (![X0 : $i]:
% 123.15/16.47         ( (in @ ('#sk337' @ X0 @ (^[Y0 : $i]: (subset @ Y0 @ X0))) @ X0)
% 123.15/16.47          |  (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3241])).
% 123.15/16.47  thf(zip_derived_cl3258, plain,
% 123.15/16.47      (![X0 : $i]:
% 123.15/16.47         (~ ('#form1598' @ X0)
% 123.15/16.47          |  (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 123.15/16.47      define([status(thm)])).
% 123.15/16.47  thf(zip_derived_cl3216, plain, ( (binintTransitive)),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3211])).
% 123.15/16.47  thf(binintTransitive, axiom, (binintTransitive) =>
% 123.15/16.47    ((((!!) @ (^[Y0 : $i]:
% 123.15/16.47                 (((transitiveset @ Y0) =>
% 123.15/16.47                   (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                               (((transitiveset @ Y1) => (transitiveset @ 
% 123.15/16.47                                 (binintersect @ Y0 @ Y1))))))))))))
% 123.15/16.47     = ($true))).
% 123.15/16.47  thf('13', plain,
% 123.15/16.47      (( binintTransitive ) <=>
% 123.15/16.47       ( ![X5:$i]:
% 123.15/16.47         ( ( transitiveset @ X5 ) =>
% 123.15/16.47           ( ![X7:$i]:
% 123.15/16.47             ( ( transitiveset @ X7 ) =>
% 123.15/16.47               ( transitiveset @ ( binintersect @ X5 @ X7 ) ) ) ) ) )),
% 123.15/16.47      inference('rw.lit', [status(esa)], [binintTransitive])).
% 123.15/16.47  thf(zip_derived_cl3223, plain,
% 123.15/16.47      ( (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                    (((transitiveset @ Y0) =>
% 123.15/16.47                      (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                                  (((transitiveset @ Y1) => (transitiveset @ 
% 123.15/16.47                                    (binintersect @ Y0 @ Y1))))))))))))),
% 123.15/16.47      inference('rw_clause', [status(thm)], [zip_derived_cl3216, '13'])).
% 123.15/16.47  thf(zip_derived_cl3229, plain,
% 123.15/16.47      (![X2 : $i]:
% 123.15/16.47          (((transitiveset @ X2) =>
% 123.15/16.47            (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                        (((transitiveset @ Y0) => (transitiveset @ 
% 123.15/16.47                          (binintersect @ X2 @ Y0)))))))))),
% 123.15/16.47      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3223])).
% 123.15/16.47  thf(zip_derived_cl3235, plain,
% 123.15/16.47      (![X2 : $i]:
% 123.15/16.47         (~ (transitiveset @ X2)
% 123.15/16.47          |  (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                         (((transitiveset @ Y0) => (transitiveset @ 
% 123.15/16.47                           (binintersect @ X2 @ Y0))))))))),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3229])).
% 123.15/16.47  thf(zip_derived_cl3242, plain,
% 123.15/16.47      (![X0 : $i]:
% 123.15/16.47         (~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0))))))
% 123.15/16.47          |  (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                         (((transitiveset @ Y0) => (transitiveset @ 
% 123.15/16.47                           (binintersect @ X0 @ Y0))))))))),
% 123.15/16.47      inference('rw_clause', [status(thm)], [zip_derived_cl3235, '12'])).
% 123.15/16.47  thf(zip_derived_cl3250, plain,
% 123.15/16.47      (![X0 : $i]:
% 123.15/16.47         ( ('#form1598' @ X0)
% 123.15/16.47          | ~ (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 123.15/16.47      define([status(thm)])).
% 123.15/16.47  thf(zip_derived_cl3293, plain, ( ('#form1598' @ '#sk1597')),
% 123.15/16.47      inference('renaming', [status(thm)],
% 123.15/16.47                [zip_derived_cl3283, zip_derived_cl3258, zip_derived_cl3250])).
% 123.15/16.47  thf(zip_derived_cl3284, plain, ( (in @ '#sk1600' @ '#sk1597')),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3277])).
% 123.15/16.47  thf(zip_derived_cl984, plain, ( (binintersectSubset2)),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl978])).
% 123.15/16.47  thf(binintersectSubset2, axiom, (binintersectSubset2) =>
% 123.15/16.47    ((((!!) @ (^[Y0 : $i]:
% 123.15/16.47                 (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                             (((subset @ Y0 @ Y1) =>
% 123.15/16.47                               (((binintersect @ Y0 @ Y1) = (Y0)))))))))))
% 123.15/16.47     = ($true))).
% 123.15/16.47  thf('14', plain,
% 123.15/16.47      (( binintersectSubset2 ) <=>
% 123.15/16.47       ( ![X5:$i,X7:$i]:
% 123.15/16.47         ( ( subset @ X5 @ X7 ) => ( ( binintersect @ X5 @ X7 ) = ( X5 ) ) ) )),
% 123.15/16.47      inference('rw.lit', [status(esa)], [binintersectSubset2])).
% 123.15/16.47  thf(zip_derived_cl992, plain,
% 123.15/16.47      ( (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                    (((!!) @ (^[Y1 : $i]:
% 123.15/16.47                                (((subset @ Y0 @ Y1) =>
% 123.15/16.47                                  (((binintersect @ Y0 @ Y1) = (Y0)))))))))))),
% 123.15/16.47      inference('rw_clause', [status(thm)], [zip_derived_cl984, '14'])).
% 123.15/16.47  thf(zip_derived_cl999, plain,
% 123.15/16.47      (![X2 : $i]:
% 123.15/16.47          (((!!) @ (^[Y0 : $i]:
% 123.15/16.47                      (((subset @ X2 @ Y0) =>
% 123.15/16.47                        (((binintersect @ X2 @ Y0) = (X2))))))))),
% 123.15/16.47      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl992])).
% 123.15/16.47  thf(zip_derived_cl1004, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47          (((subset @ X2 @ X4) => (((binintersect @ X2 @ X4) = (X2)))))),
% 123.15/16.47      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl999])).
% 123.15/16.47  thf(zip_derived_cl1009, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         (~ (subset @ X2 @ X4) |  (((binintersect @ X2 @ X4) = (X2))))),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl1004])).
% 123.15/16.47  thf(zip_derived_cl1015, plain,
% 123.15/16.47      (![X2 : $i, X4 : $i]:
% 123.15/16.47         (~ (subset @ X2 @ X4) | ((binintersect @ X2 @ X4) = (X2)))),
% 123.15/16.47      inference('simplify nested equalities', [status(thm)],
% 123.15/16.47                [zip_derived_cl1009])).
% 123.15/16.47  thf(zip_derived_cl3258, plain,
% 123.15/16.47      (![X0 : $i]:
% 123.15/16.47         (~ ('#form1598' @ X0)
% 123.15/16.47          |  (((!!) @ (^[Y0 : $i]: (((in @ Y0 @ X0) => (subset @ Y0 @ X0)))))))),
% 123.15/16.47      define([status(thm)])).
% 123.15/16.47  thf(zip_derived_cl3259, plain,
% 123.15/16.47      (![X0 : $i, X2 : $i]:
% 123.15/16.47         ( (((in @ X2 @ X0) => (subset @ X2 @ X0))) | ~ ('#form1598' @ X0))),
% 123.15/16.47      inference('lazy_cnf_forall', [status(thm)], [zip_derived_cl3258])).
% 123.15/16.47  thf(zip_derived_cl3270, plain,
% 123.15/16.47      (![X0 : $i, X2 : $i]:
% 123.15/16.47         (~ (in @ X2 @ X0) |  (subset @ X2 @ X0) | ~ ('#form1598' @ X0))),
% 123.15/16.47      inference('lazy_cnf_imply', [status(thm)], [zip_derived_cl3259])).
% 123.15/16.47  thf(zip_derived_cl17314, plain, ($false),
% 123.15/16.47      inference('eprover', [status(thm)],
% 123.15/16.47                [zip_derived_cl3294, zip_derived_cl3295, zip_derived_cl1113, 
% 123.15/16.47                 zip_derived_cl1023, zip_derived_cl3419, zip_derived_cl3293, 
% 123.15/16.47                 zip_derived_cl3284, zip_derived_cl1015, zip_derived_cl3270])).
% 123.15/16.47  
% 123.15/16.47  % SZS output end Refutation
% 123.15/16.47  
% 123.15/16.47  
% 123.15/16.47  % /export/starexec/sandbox/solver/bin/lams/35_full_unif.sh running for 56s
% 123.15/16.47  % Terminating...
% 124.73/16.77  % Runner terminated.
% 124.73/16.78  % Zipperpin 1.5 exiting
%------------------------------------------------------------------------------